NALOGA2
Rebeka Šumrada
2024-01-08
- Najprej uvozimo podatke. Določene spremenljivke izločimo, saj so irelevantne za naša raziskovalna vprašanja. Za lažje posploševanje spremenljivki ocena v 1. in ocena v 2. semestru spremenimo v eno spremenljivko, ki predstavlja povprečje omenjenih. Poimenujemo jo grade_average.
podatki<-read.csv("student_data.csv", header=TRUE, sep = ";")
podatki <- podatki[,c(1,5,13,16,17,18,24,30)]
podatki$grade_average<-(podatki$Curricular.units.1st.sem..grade. + podatki$Curricular.units.2nd.sem..grade.)/2
round(podatki$Curricular.units.1st.sem..grade.,2)## [1] 0.00 14.00 0.00 13.43 12.33 11.86 13.30 0.00 13.88 11.40 12.33 13.21
## [13] 0.00 10.57 13.25 13.20 12.00 13.31 12.50 11.67 0.00 11.44 12.86 13.38
## [25] 13.30 11.60 11.38 12.67 12.00 12.93 11.86 12.83 11.33 12.67 12.40 0.00
## [37] 0.00 10.00 11.00 11.67 12.75 14.80 13.93 13.00 0.00 11.50 11.67 13.52
## [49] 11.50 12.33 13.67 11.83 14.00 14.71 10.60 13.04 0.00 13.00 14.94 0.00
## [61] 13.13 12.00 0.00 11.40 0.00 11.90 0.00 12.57 11.20 12.00 0.00 11.97
## [73] 0.00 11.67 12.33 10.33 10.50 13.67 14.84 12.00 12.20 0.00 12.17 12.00
## [85] 11.00 13.08 10.50 10.67 14.00 10.00 0.00 14.00 12.00 12.67 11.88 14.00
## [97] 13.67 13.75 14.20 11.96 12.88 0.00 0.00 14.63 0.00 13.00 0.00 14.20
## [109] 13.27 11.67 13.86 13.00 13.40 12.67 12.52 11.62 10.00 10.33 13.14 12.60
## [121] 11.00 10.80 0.00 12.80 14.17 12.10 14.17 12.80 13.00 13.47 13.24 12.33
## [133] 12.40 14.00 11.67 12.00 12.20 14.83 13.19 17.12 12.67 12.67 0.00 11.33
## [145] 13.61 12.00 0.00 11.20 13.38 13.86 0.00 12.40 12.33 13.33 12.67 12.00
## [157] 10.60 12.25 11.00 11.00 13.17 12.86 14.92 11.50 14.20 12.50 0.00 11.67
## [169] 14.26 12.00 11.25 12.46 11.68 11.67 11.75 11.67 13.20 11.95 12.40 14.35
## [181] 12.62 12.67 12.00 12.17 0.00 10.00 11.50 13.05 11.00 11.50 12.00 10.00
## [193] 0.00 0.00 12.24 0.00 12.93 0.00 12.57 11.82 13.75 11.17 12.32 12.17
## [205] 11.14 11.00 12.91 13.83 13.86 13.71 12.64 12.92 15.62 0.00 11.71 12.12
## [217] 11.60 10.00 10.00 0.00 13.00 13.33 11.25 13.85 13.74 15.33 11.00 12.00
## [229] 0.00 11.57 12.86 0.00 13.00 11.00 12.00 12.60 13.40 11.33 13.50 11.75
## [241] 12.47 12.91 11.60 0.00 12.90 13.22 13.15 12.75 11.33 13.25 12.40 15.00
## [253] 14.40 11.00 12.40 16.00 13.57 11.83 11.67 11.83 11.17 0.00 11.75 14.00
## [265] 12.83 12.25 14.83 11.40 13.00 13.67 12.67 10.00 13.50 12.67 14.50 13.69
## [277] 11.00 11.56 13.80 14.00 12.00 14.17 14.00 13.80 12.80 12.17 12.50 12.00
## [289] 10.83 13.38 15.67 14.33 11.43 11.67 12.00 14.73 14.17 11.57 12.50 12.86
## [301] 12.25 12.00 15.12 12.50 0.00 11.00 11.88 11.00 15.20 11.60 14.83 11.33
## [313] 11.20 13.40 10.50 16.20 14.54 13.69 11.29 11.76 0.00 13.06 14.30 11.80
## [325] 10.33 10.57 13.33 11.86 12.60 14.00 12.00 0.00 12.00 12.67 12.17 13.33
## [337] 15.00 13.39 12.17 11.25 12.00 0.00 12.83 14.00 13.00 13.50 10.69 11.00
## [349] 13.00 12.00 12.60 13.67 0.00 14.20 11.00 15.00 12.59 0.00 0.00 0.00
## [361] 11.67 12.67 10.33 13.50 13.98 16.15 14.03 11.00 13.86 13.41 13.55 11.25
## [373] 13.83 12.00 0.00 11.90 0.00 15.14 12.29 12.67 12.74 13.25 10.33 13.43
## [385] 12.56 11.50 13.67 11.27 13.17 14.67 12.75 11.20 13.00 10.50 14.86 12.86
## [397] 11.73 13.14 11.80 10.67 11.60 10.33 12.25 12.00 14.73 0.00 13.62 15.80
## [409] 14.67 0.00 14.65 12.40 11.59 14.00 12.33 14.00 15.23 11.60 11.60 0.00
## [421] 12.90 14.14 0.00 13.25 13.79 13.92 13.50 11.33 0.00 11.50 12.08 11.83
## [433] 13.40 0.00 14.20 13.81 11.25 14.50 0.00 11.30 0.00 12.00 12.30 12.69
## [445] 11.00 13.00 14.41 12.93 13.33 12.80 14.40 13.38 14.13 11.71 11.80 11.17
## [457] 0.00 13.60 13.85 12.50 16.40 13.82 10.60 10.20 10.60 11.44 14.33 13.00
## [469] 13.31 10.57 13.49 12.33 11.88 13.97 0.00 11.50 12.50 0.00 11.98 13.20
## [481] 11.61 14.31 0.00 12.67 12.77 12.67 11.50 11.40 14.71 11.81 13.00 14.86
## [493] 12.60 13.33 10.67 11.50 10.00 11.80 11.80 12.77 11.33 12.67 12.20 12.00
## [505] 11.72 14.00 14.75 12.67 13.00 0.00 10.75 0.00 12.50 0.00 0.00 0.00
## [517] 12.50 12.80 10.00 11.25 12.61 12.00 13.00 12.00 12.00 12.00 12.00 0.00
## [529] 0.00 13.62 11.67 0.00 11.69 0.00 0.00 11.50 14.00 11.00 12.86 12.50
## [541] 14.53 10.00 13.00 15.96 13.20 10.20 14.20 12.62 13.50 13.25 12.00 13.00
## [553] 11.78 11.00 0.00 12.43 11.00 0.00 11.50 12.51 12.09 11.00 10.00 13.50
## [565] 14.17 14.00 0.00 11.67 14.60 13.00 12.17 0.00 10.50 12.40 0.00 0.00
## [577] 13.83 10.60 11.50 13.50 0.00 12.54 14.83 12.00 11.80 15.00 12.00 12.83
## [589] 11.67 12.16 13.83 12.45 12.12 13.40 13.33 11.45 12.00 12.67 12.67 11.89
## [601] 0.00 13.00 16.89 12.50 13.06 0.00 0.00 12.36 0.00 11.98 13.86 13.00
## [613] 12.83 11.00 12.36 13.86 12.33 12.85 12.34 12.67 13.83 10.75 13.25 13.73
## [625] 13.33 12.00 10.89 13.03 13.00 11.80 12.04 12.20 12.84 11.00 13.50 12.12
## [637] 12.63 10.67 11.20 12.67 13.50 11.67 10.50 14.27 0.00 10.50 11.20 12.00
## [649] 12.23 11.50 15.38 13.67 12.61 12.20 11.75 11.40 10.60 10.92 12.40 0.00
## [661] 15.83 11.80 12.57 12.00 13.36 15.40 12.20 12.82 0.00 13.39 14.25 13.44
## [673] 12.29 11.67 12.17 10.00 14.00 11.83 15.00 0.00 10.83 13.14 14.40 0.00
## [685] 12.00 12.20 12.33 11.84 11.80 0.00 0.00 12.68 12.57 11.25 14.00 13.33
## [697] 13.67 10.00 12.60 17.33 13.20 14.00 13.88 0.00 13.11 13.00 12.50 14.11
## [709] 14.73 0.00 0.00 0.00 13.50 13.11 13.50 11.85 0.00 14.33 15.80 13.80
## [721] 12.67 13.00 0.00 11.00 0.00 15.20 14.43 0.00 0.00 13.75 12.17 12.14
## [733] 12.00 11.67 0.00 11.88 11.29 10.00 12.00 13.83 0.00 14.43 14.20 11.50
## [745] 13.00 0.00 11.33 12.50 0.00 13.47 11.75 13.33 13.11 0.00 15.50 0.00
## [757] 11.25 11.00 12.33 11.38 12.22 0.00 12.00 11.00 14.12 10.20 12.00 12.33
## [769] 14.33 15.17 15.14 0.00 13.41 12.33 11.80 12.00 15.00 13.88 11.83 12.50
## [781] 15.00 11.67 14.67 13.35 12.80 10.83 13.67 14.54 14.40 0.00 13.17 11.50
## [793] 11.33 12.00 13.17 14.83 13.00 13.09 13.33 12.17 11.00 0.00 13.60 15.50
## [805] 13.86 11.50 13.00 14.00 0.00 11.17 0.00 12.14 14.15 14.45 15.71 12.80
## [817] 12.50 14.50 13.46 12.83 12.00 0.00 14.71 12.57 12.50 14.00 11.57 15.83
## [829] 14.25 0.00 11.67 0.00 13.20 12.00 0.00 12.00 13.33 12.41 0.00 13.80
## [841] 0.00 11.50 0.00 14.02 11.40 0.00 10.40 10.67 14.25 13.91 13.76 12.60
## [853] 13.86 13.84 0.00 11.80 12.67 0.00 0.00 10.75 12.60 0.00 12.00 14.00
## [865] 14.00 14.68 0.00 0.00 13.86 0.00 13.14 18.00 11.46 11.20 15.00 14.24
## [877] 11.50 10.00 12.33 12.20 13.67 0.00 11.00 13.00 12.60 12.20 13.17 11.00
## [889] 14.01 13.00 14.00 0.00 14.43 0.00 11.83 11.33 12.50 13.33 10.83 13.00
## [901] 10.00 11.43 12.89 12.95 10.00 13.09 0.00 11.71 11.25 0.00 13.17 12.75
## [913] 10.60 11.20 0.00 13.00 0.00 0.00 14.17 12.83 11.75 10.83 11.75 11.50
## [925] 10.00 13.70 14.00 11.38 0.00 0.00 11.00 13.00 13.60 11.00 11.71 13.25
## [937] 10.75 12.00 12.67 11.40 13.00 14.00 0.00 0.00 15.29 13.17 13.60 0.00
## [949] 11.40 0.00 11.00 0.00 13.57 0.00 11.25 13.33 12.00 12.50 13.20 0.00
## [961] 11.67 13.47 13.67 11.67 11.67 13.40 0.00 0.00 0.00 10.67 13.75 10.00
## [973] 0.00 16.00 12.29 12.00 12.67 11.80 10.60 11.90 11.25 11.00 12.00 11.75
## [985] 10.00 13.71 14.88 10.80 12.00 12.50 14.73 12.00 11.43 14.17 12.50 14.17
## [997] 14.46 12.80 12.67 12.50 0.00 0.00 0.00 11.20 16.50 13.67 15.23 12.78
## [1009] 14.43 13.88 13.13 11.61 14.60 0.00 11.80 12.33 11.00 13.18 11.00 11.83
## [1021] 12.98 11.33 11.68 14.50 13.14 11.50 14.20 11.67 13.18 13.31 10.60 12.00
## [1033] 13.43 13.25 13.00 14.33 0.00 14.00 12.00 12.33 11.80 12.79 11.62 11.99
## [1045] 11.60 0.00 13.17 14.10 12.40 15.01 0.00 14.05 14.85 13.00 14.79 13.70
## [1057] 12.50 14.57 11.20 12.69 13.57 0.00 11.00 14.45 13.60 14.00 13.42 12.33
## [1069] 13.10 13.20 14.75 13.14 12.50 13.75 12.40 13.33 11.73 12.50 0.00 13.53
## [1081] 13.17 13.20 12.20 13.43 12.71 0.00 13.67 11.00 11.40 0.00 12.00 0.00
## [1093] 11.00 12.00 13.31 13.67 0.00 12.20 12.67 14.07 14.25 0.00 12.00 11.17
## [1105] 13.00 0.00 14.90 12.65 11.00 12.40 12.00 12.14 12.62 10.67 13.77 13.12
## [1117] 0.00 12.70 11.86 12.33 15.75 13.33 14.36 13.00 12.83 13.20 17.01 10.60
## [1129] 14.00 12.11 13.06 13.29 11.00 14.07 0.00 11.25 14.00 12.17 13.30 13.92
## [1141] 13.37 12.40 15.00 13.33 12.00 13.40 0.00 11.50 12.00 13.49 12.00 0.00
## [1153] 10.33 12.94 13.26 12.25 11.67 13.57 11.80 14.20 11.00 13.62 14.65 11.33
## [1165] 13.70 13.73 11.75 12.33 14.00 11.50 11.20 15.07 10.00 12.00 13.00 11.00
## [1177] 13.57 14.60 11.83 12.62 11.50 13.25 12.61 13.75 13.60 11.14 12.70 10.00
## [1189] 11.67 14.00 0.00 12.04 0.00 13.77 15.44 11.50 10.00 12.25 14.50 15.57
## [1201] 15.57 13.80 10.67 11.60 13.00 12.00 12.33 12.88 11.00 12.25 0.00 10.75
## [1213] 13.63 13.00 13.53 16.90 12.00 12.50 12.76 13.75 0.00 14.60 0.00 13.83
## [1225] 13.58 15.14 10.67 11.20 13.76 13.25 10.71 12.17 14.36 12.83 13.93 12.00
## [1237] 13.44 16.00 13.12 0.00 11.40 11.00 11.00 13.67 11.75 10.00 13.50 0.00
## [1249] 12.00 13.00 14.83 11.83 12.00 12.75 0.00 0.00 12.00 11.68 13.60 16.00
## [1261] 11.80 0.00 0.00 16.14 11.79 13.42 12.50 12.46 12.38 10.00 12.60 12.60
## [1273] 10.00 0.00 11.60 12.17 13.60 12.50 12.25 11.71 13.50 13.02 0.00 17.33
## [1285] 11.00 13.67 11.38 12.83 12.60 14.33 13.50 14.29 11.75 14.80 0.00 10.00
## [1297] 0.00 12.60 12.43 10.00 12.33 0.00 0.00 12.10 14.71 12.67 14.38 13.40
## [1309] 13.31 11.99 11.55 16.46 13.67 12.65 12.33 14.37 12.00 12.00 12.00 12.60
## [1321] 12.17 13.50 13.76 12.40 10.67 14.33 12.50 10.00 14.70 11.50 12.86 13.70
## [1333] 0.00 11.20 13.29 13.00 12.60 12.80 11.50 11.40 12.33 12.80 12.00 13.00
## [1345] 11.83 14.00 12.33 13.04 13.17 12.50 0.00 15.66 12.17 0.00 10.60 13.43
## [1357] 11.75 0.00 0.00 0.00 13.00 13.33 0.00 0.00 13.70 0.00 13.45 12.20
## [1369] 10.00 13.00 12.00 15.03 12.00 12.00 13.67 0.00 12.00 0.00 14.00 0.00
## [1381] 12.38 0.00 11.42 13.35 15.00 10.50 0.00 13.25 0.00 11.50 13.88 11.33
## [1393] 0.00 12.86 11.60 11.40 13.33 13.57 11.83 14.43 0.00 12.29 14.40 13.15
## [1405] 0.00 0.00 12.34 12.20 10.50 10.60 0.00 11.25 10.50 11.00 13.46 12.60
## [1417] 0.00 13.67 11.60 12.57 11.80 11.60 11.33 10.67 13.50 0.00 13.33 13.40
## [1429] 10.20 13.00 12.91 12.00 10.83 15.33 12.82 13.00 13.50 12.50 13.00 11.75
## [1441] 12.50 11.61 14.00 0.00 13.80 0.00 0.00 12.25 11.50 12.57 12.00 12.00
## [1453] 0.00 12.00 11.60 0.00 12.00 13.98 12.50 0.00 10.50 12.86 11.67 13.00
## [1465] 11.83 12.45 11.00 13.20 15.50 12.33 12.00 11.60 11.33 0.00 12.00 12.00
## [1477] 12.50 13.67 14.50 13.20 12.17 11.25 15.17 11.17 10.98 10.75 13.38 11.29
## [1489] 0.00 13.00 16.11 11.50 10.75 11.60 0.00 13.80 13.59 13.86 12.00 13.44
## [1501] 14.00 12.00 14.20 13.34 12.46 11.00 10.50 0.00 14.00 0.00 0.00 10.00
## [1513] 0.00 13.50 0.00 13.39 0.00 13.58 0.00 0.00 10.00 15.20 12.80 11.17
## [1525] 0.00 12.83 12.50 10.00 11.50 11.33 13.00 13.03 12.17 14.50 14.40 12.25
## [1537] 0.00 12.67 12.00 0.00 11.67 0.00 10.00 0.00 12.25 12.00 12.60 0.00
## [1549] 0.00 0.00 12.69 10.40 10.47 14.33 14.67 12.84 0.00 0.00 0.00 13.25
## [1561] 12.86 13.60 14.00 12.00 13.17 13.62 14.85 10.75 0.00 0.00 14.00 0.00
## [1573] 0.00 13.00 12.38 0.00 11.40 11.25 13.00 0.00 13.50 11.00 0.00 12.00
## [1585] 13.00 0.00 12.00 11.17 10.50 12.67 11.00 0.00 11.50 0.00 10.50 12.50
## [1597] 12.83 15.57 12.00 11.25 0.00 12.29 11.00 12.14 11.50 12.55 13.00 12.89
## [1609] 12.67 12.83 10.67 13.00 11.98 0.00 11.83 12.67 13.75 11.40 13.17 12.83
## [1621] 14.12 11.67 10.25 12.51 11.50 10.00 15.71 12.50 12.00 0.00 12.25 0.00
## [1633] 13.60 13.31 12.20 12.29 12.00 13.34 0.00 14.27 12.14 14.17 13.53 12.00
## [1645] 11.40 0.00 12.92 13.64 12.90 14.36 14.51 14.70 15.20 13.00 13.50 12.33
## [1657] 13.40 11.75 0.00 0.00 14.73 16.57 15.14 13.44 14.17 14.00 11.33 13.76
## [1669] 11.60 12.75 12.50 15.31 13.29 14.76 12.77 10.40 0.00 10.50 14.25 11.92
## [1681] 10.67 12.25 12.00 11.00 14.17 14.67 0.00 12.67 0.00 0.00 0.00 0.00
## [1693] 13.70 11.80 0.00 13.33 11.40 0.00 16.14 0.00 15.63 13.67 0.00 12.50
## [1705] 12.29 14.00 0.00 10.75 12.95 12.45 12.25 13.38 12.16 12.50 12.75 13.34
## [1717] 14.18 10.00 0.00 0.00 12.00 10.57 14.15 11.17 12.00 11.33 12.59 12.00
## [1729] 0.00 12.25 11.60 13.00 10.67 12.33 11.00 13.43 13.05 12.04 14.17 0.00
## [1741] 13.60 12.20 13.71 11.67 14.00 12.50 11.83 0.00 0.00 11.54 11.29 0.00
## [1753] 11.80 0.00 0.00 14.20 12.70 12.67 14.43 13.12 12.67 0.00 15.29 10.50
## [1765] 12.64 0.00 14.33 15.12 0.00 12.00 14.25 10.50 13.50 11.67 10.80 0.00
## [1777] 12.80 10.80 11.40 13.73 12.80 13.50 15.57 11.00 14.11 11.00 0.00 13.50
## [1789] 11.25 12.14 13.08 0.00 11.00 0.00 13.12 13.51 12.83 15.00 12.80 12.33
## [1801] 12.29 12.33 11.50 11.83 0.00 0.00 11.80 0.00 12.20 12.33 12.43 12.77
## [1813] 12.10 12.00 0.00 14.89 11.36 13.50 0.00 13.88 13.00 12.65 11.00 11.67
## [1825] 14.50 14.71 13.29 11.33 0.00 11.57 13.00 11.50 11.80 10.67 13.89 11.40
## [1837] 12.33 12.16 13.43 15.17 0.00 10.50 11.80 13.20 13.07 11.60 13.67 10.75
## [1849] 13.49 12.50 0.00 13.29 12.60 14.00 11.50 0.00 11.83 11.50 14.17 12.50
## [1861] 0.00 0.00 10.50 11.83 0.00 12.40 10.50 0.00 14.58 11.67 0.00 13.00
## [1873] 15.66 0.00 12.17 13.30 0.00 0.00 0.00 13.56 14.33 12.00 0.00 0.00
## [1885] 11.75 12.18 11.83 0.00 15.00 0.00 0.00 13.44 13.50 0.00 11.50 10.50
## [1897] 12.00 12.20 0.00 14.50 13.33 12.00 15.12 13.12 12.83 13.33 13.88 12.94
## [1909] 12.33 14.27 13.00 12.48 13.43 10.67 15.40 13.45 12.60 12.49 10.80 12.20
## [1921] 14.20 13.83 12.80 13.20 14.00 13.88 12.50 13.43 11.80 14.87 13.03 14.57
## [1933] 11.00 13.37 12.81 13.92 13.00 13.68 13.00 12.80 13.57 13.17 15.00 12.67
## [1945] 13.86 14.69 14.04 11.00 13.33 11.77 0.00 0.00 0.00 12.29 12.46 12.17
## [1957] 11.83 14.81 10.60 13.12 12.83 0.00 13.00 12.72 11.25 13.82 12.33 12.33
## [1969] 13.25 13.67 12.62 14.83 11.20 11.40 13.13 13.00 12.85 13.50 14.29 13.50
## [1981] 10.75 11.33 13.00 13.97 14.14 11.60 14.66 0.00 12.99 11.25 12.20 0.00
## [1993] 11.33 12.20 0.00 11.33 13.86 12.86 10.00 10.21 11.29 13.83 12.86 11.67
## [2005] 0.00 14.40 14.83 14.33 0.00 0.00 12.33 11.80 13.20 0.00 0.00 11.50
## [2017] 12.60 13.54 11.60 13.67 0.00 0.00 0.00 11.50 11.50 11.83 0.00 0.00
## [2029] 12.97 13.83 14.13 12.17 12.67 0.00 12.29 14.50 10.00 11.50 11.60 12.50
## [2041] 11.67 13.43 13.67 12.50 13.00 12.78 0.00 13.50 13.46 13.44 11.00 11.33
## [2053] 10.00 13.44 12.21 14.17 12.85 13.00 12.80 13.00 13.37 13.39 13.33 14.00
## [2065] 12.60 14.00 13.43 13.00 12.67 10.00 12.83 12.92 13.29 14.60 14.00 14.14
## [2077] 11.67 14.38 12.50 14.15 12.47 14.15 14.07 14.86 14.29 0.00 0.00 15.00
## [2089] 12.63 11.20 14.23 12.20 15.70 15.20 16.33 12.56 0.00 12.40 13.78 12.17
## [2101] 11.80 10.80 13.26 12.00 11.88 12.16 15.00 13.33 11.50 14.43 13.00 15.00
## [2113] 15.16 10.67 11.00 0.00 12.29 12.83 12.67 0.00 13.00 10.88 12.80 11.29
## [2125] 0.00 0.00 13.77 12.76 0.00 12.67 12.00 12.25 11.33 13.51 13.61 0.00
## [2137] 11.50 12.33 11.97 13.00 12.39 13.50 12.17 0.00 11.67 12.40 13.40 12.00
## [2149] 14.20 12.12 13.86 11.75 14.28 13.27 14.67 15.11 0.00 15.00 13.20 11.00
## [2161] 14.57 12.00 0.00 13.80 14.83 12.83 14.96 12.00 12.40 15.57 13.71 13.14
## [2173] 15.00 13.00 12.00 0.00 15.17 12.00 13.64 12.67 0.00 10.80 14.25 12.15
## [2185] 11.50 12.25 12.00 13.40 11.33 12.20 0.00 0.00 16.17 11.00 0.00 12.00
## [2197] 10.50 11.67 11.00 0.00 12.50 11.29 11.20 0.00 13.20 14.14 0.00 0.00
## [2209] 12.33 0.00 13.10 13.50 10.20 11.57 15.29 12.60 13.43 11.60 14.67 14.67
## [2221] 12.74 11.97 12.25 0.00 14.94 10.50 13.33 0.00 13.80 11.83 0.00 0.00
## [2233] 10.00 11.50 10.67 0.00 12.75 0.00 11.33 0.00 13.00 10.75 12.00 13.46
## [2245] 10.00 12.33 12.53 0.00 0.00 13.60 12.33 11.45 13.50 0.00 11.00 13.71
## [2257] 12.36 10.67 12.00 12.86 13.12 0.00 13.50 15.09 12.40 14.00 13.50 0.00
## [2269] 12.65 0.00 0.00 13.33 11.33 0.00 0.00 11.67 12.17 13.33 11.40 12.14
## [2281] 13.06 11.75 11.83 12.40 13.43 0.00 11.00 13.62 11.80 0.00 15.00 10.80
## [2293] 13.67 12.83 0.00 15.12 0.00 11.40 12.25 0.00 14.00 12.33 10.67 11.83
## [2305] 0.00 11.67 13.00 0.00 0.00 13.00 13.86 13.39 12.75 14.50 12.17 15.40
## [2317] 13.33 0.00 0.00 13.71 12.25 16.00 11.00 14.09 10.17 10.00 0.00 10.50
## [2329] 0.00 0.00 0.00 0.00 13.33 0.00 13.57 12.83 10.25 0.00 14.50 15.80
## [2341] 0.00 12.50 11.67 13.00 12.12 14.22 12.50 12.17 0.00 12.67 13.61 12.86
## [2353] 14.00 14.75 0.00 13.62 0.00 11.80 15.12 11.50 10.00 0.00 10.33 0.00
## [2365] 12.00 13.83 12.15 14.00 16.50 18.00 11.29 0.00 0.00 14.00 13.75 13.25
## [2377] 14.25 0.00 11.25 13.50 12.67 15.17 13.17 11.80 11.50 14.50 13.40 0.00
## [2389] 10.80 0.00 11.43 12.50 13.50 0.00 12.75 11.33 0.00 11.40 14.43 12.49
## [2401] 11.50 11.20 12.00 15.89 12.94 14.00 0.00 0.00 0.00 11.25 0.00 11.25
## [2413] 10.67 11.80 11.62 0.00 10.25 10.80 12.55 13.57 0.00 0.00 14.78 0.00
## [2425] 0.00 0.00 0.00 11.40 11.67 11.29 11.50 16.00 12.50 12.00 0.00 13.00
## [2437] 13.71 12.33 12.73 14.00 0.00 11.40 0.00 18.88 0.00 11.33 13.50 15.00
## [2449] 0.00 14.22 0.00 12.00 12.60 15.08 0.00 14.50 14.50 10.00 0.00 11.60
## [2461] 11.75 0.00 0.00 0.00 11.25 11.57 10.00 13.83 12.75 0.00 11.60 0.00
## [2473] 11.25 0.00 14.33 0.00 13.50 12.67 12.44 10.67 0.00 12.67 13.20 12.70
## [2485] 14.83 11.50 0.00 0.00 12.67 14.71 13.67 10.80 10.50 15.00 12.67 13.17
## [2497] 0.00 13.00 0.00 10.00 13.33 12.33 13.18 12.51 0.00 13.59 11.16 11.86
## [2509] 0.00 14.00 12.00 11.57 13.20 13.50 13.33 14.25 12.17 12.21 12.67 12.29
## [2521] 13.00 12.14 13.88 0.00 11.67 13.15 14.50 14.44 15.17 11.60 11.67 12.62
## [2533] 12.67 12.83 11.86 11.40 14.86 14.71 13.50 11.50 14.00 12.83 13.43 0.00
## [2545] 11.67 16.00 13.83 13.23 14.00 10.00 13.33 12.50 12.50 10.50 10.67 10.50
## [2557] 12.00 0.00 11.50 14.00 13.50 13.07 10.75 12.00 14.00 12.33 13.46 10.67
## [2569] 11.60 13.67 14.40 15.47 12.62 14.98 15.00 15.89 11.50 10.50 13.98 13.00
## [2581] 13.67 0.00 14.40 12.00 14.17 12.20 12.00 10.50 12.33 12.20 0.00 11.50
## [2593] 10.89 12.17 10.00 12.67 11.40 0.00 13.00 13.40 13.50 12.25 12.29 0.00
## [2605] 10.50 14.00 14.20 13.00 11.00 11.00 12.39 14.75 16.17 0.00 12.40 11.60
## [2617] 12.20 11.00 12.33 14.83 11.56 12.00 12.73 10.50 12.33 0.00 14.84 12.20
## [2629] 10.80 12.75 11.00 10.75 12.55 12.67 12.71 11.75 11.00 0.00 13.40 12.58
## [2641] 0.00 12.00 12.33 11.50 12.80 0.00 13.29 11.80 11.33 12.00 13.98 15.20
## [2653] 13.14 0.00 13.87 12.68 0.00 12.00 0.00 11.00 10.75 14.20 12.60 0.00
## [2665] 14.00 10.00 13.83 11.00 11.64 12.25 12.50 13.80 12.00 11.00 13.75 10.67
## [2677] 0.00 13.83 0.00 15.80 12.53 12.78 0.00 13.00 0.00 10.80 11.00 0.00
## [2689] 0.00 12.00 10.75 11.60 11.80 16.00 12.67 14.40 0.00 12.25 12.60 13.40
## [2701] 0.00 10.00 0.00 11.25 0.00 10.67 11.75 0.00 12.67 11.95 14.00 0.00
## [2713] 11.50 12.00 16.43 13.34 0.00 14.67 14.12 14.86 13.83 11.00 11.75 10.00
## [2725] 12.41 11.00 14.43 14.31 15.43 12.00 13.83 12.17 14.01 10.33 13.20 15.40
## [2737] 13.39 10.86 11.33 14.50 14.17 12.83 13.33 13.67 10.83 13.43 12.40 0.00
## [2749] 0.00 11.50 0.00 14.14 0.00 13.80 13.60 11.73 10.00 0.00 0.00 10.80
## [2761] 13.05 11.00 12.33 11.80 11.00 13.11 14.41 0.00 12.33 0.00 14.10 13.04
## [2773] 12.86 14.25 14.06 15.08 0.00 13.75 13.15 12.33 13.78 10.33 11.33 13.20
## [2785] 13.57 12.75 13.00 11.33 0.00 0.00 12.50 14.86 12.00 0.00 0.00 12.83
## [2797] 0.00 13.33 13.07 12.00 15.50 0.00 14.71 16.71 10.86 11.66 11.60 14.62
## [2809] 12.17 13.38 12.50 12.56 13.19 11.00 0.00 11.60 14.27 11.00 12.67 0.00
## [2821] 12.77 0.00 15.50 13.29 11.72 11.33 13.33 12.33 12.33 0.00 12.60 12.60
## [2833] 14.33 12.00 14.86 11.92 0.00 13.33 0.00 17.00 11.67 12.21 13.00 0.00
## [2845] 10.50 13.57 14.00 0.00 12.46 14.40 0.00 14.33 11.91 13.71 0.00 13.46
## [2857] 15.00 0.00 13.40 13.00 11.25 12.60 12.67 12.33 12.00 16.40 0.00 12.75
## [2869] 14.50 14.80 10.37 0.00 10.67 12.69 0.00 11.80 0.00 12.33 13.00 12.50
## [2881] 12.20 11.00 10.00 12.33 14.31 14.45 11.00 13.14 13.75 14.00 13.75 0.00
## [2893] 13.17 12.44 12.67 11.33 11.25 13.61 12.41 0.00 11.50 0.00 11.00 14.00
## [2905] 12.00 12.50 11.33 14.07 13.56 11.60 0.00 13.28 0.00 14.38 0.00 10.67
## [2917] 13.42 12.97 10.93 0.00 0.00 13.25 11.33 11.00 12.76 14.50 13.83 11.25
## [2929] 0.00 13.67 0.00 13.00 0.00 11.97 0.00 16.00 0.00 12.75 11.00 0.00
## [2941] 12.20 12.43 14.50 13.00 11.71 10.25 0.00 12.38 12.67 10.50 14.12 14.67
## [2953] 11.40 0.00 14.00 0.00 0.00 12.64 12.33 15.00 11.75 14.14 12.00 10.80
## [2965] 13.29 13.60 13.55 0.00 13.50 11.60 12.50 11.00 12.00 11.60 0.00 14.64
## [2977] 13.00 12.79 14.50 14.60 12.50 14.00 13.80 14.43 14.35 14.33 12.25 13.33
## [2989] 13.00 11.75 14.50 11.82 0.00 12.40 12.57 13.86 11.83 11.00 14.67 0.00
## [3001] 12.71 13.42 14.00 12.14 12.80 14.57 11.25 10.00 14.40 12.98 15.75 12.29
## [3013] 13.76 13.83 0.00 14.71 14.62 13.68 13.17 10.80 12.00 13.96 13.00 0.00
## [3025] 0.00 14.00 12.57 12.00 13.62 12.50 12.43 13.39 12.65 14.00 12.80 11.33
## [3037] 0.00 14.17 12.83 12.00 13.00 13.39 12.33 12.57 12.33 13.00 12.33 13.17
## [3049] 13.33 13.00 10.90 11.50 15.86 12.60 14.00 14.67 13.67 0.00 12.63 14.23
## [3061] 15.00 10.00 12.25 13.50 12.20 0.00 12.00 12.32 12.35 0.00 11.33 0.00
## [3073] 11.60 12.00 11.75 12.80 11.33 0.00 10.80 12.50 15.20 13.31 13.09 0.00
## [3085] 12.20 12.83 11.20 12.33 15.94 0.00 10.25 13.20 14.17 14.57 10.00 12.29
## [3097] 14.00 11.25 11.60 12.00 13.47 12.40 11.75 0.00 12.00 15.33 12.32 13.80
## [3109] 13.17 16.33 0.00 14.76 11.67 12.60 11.67 15.00 0.00 13.57 10.80 11.33
## [3121] 11.40 10.64 10.50 14.65 13.71 12.27 10.38 11.00 13.80 12.67 11.75 12.79
## [3133] 14.44 13.25 12.51 0.00 12.75 16.86 13.17 12.20 16.50 11.75 11.00 15.11
## [3145] 15.50 11.14 11.33 12.04 11.17 10.60 12.50 0.00 15.67 15.33 12.18 10.00
## [3157] 12.00 10.33 11.17 11.00 0.00 12.86 14.33 15.00 13.60 12.86 14.50 10.67
## [3169] 13.43 11.72 12.00 13.20 12.20 12.58 11.33 0.00 12.43 13.00 14.54 11.20
## [3181] 16.00 13.14 11.69 10.50 13.83 0.00 0.00 0.00 10.00 0.00 0.00 12.60
## [3193] 11.25 12.38 10.71 0.00 12.00 12.60 0.00 12.84 0.00 14.17 12.17 10.80
## [3205] 13.00 0.00 13.00 11.57 11.50 11.00 17.11 0.00 12.57 0.00 14.50 13.50
## [3217] 11.20 10.67 11.00 0.00 10.00 12.36 15.25 0.00 13.00 13.81 13.29 11.50
## [3229] 11.96 13.68 14.99 11.25 12.50 0.00 13.78 13.80 13.80 12.67 14.42 13.17
## [3241] 10.67 12.07 10.25 14.11 12.40 12.00 14.83 15.43 11.60 14.17 9.80 10.71
## [3253] 0.00 12.33 13.00 11.40 12.77 12.60 13.00 14.32 12.75 13.40 0.00 15.75
## [3265] 12.40 11.50 13.40 11.67 0.00 13.29 11.50 13.25 12.25 12.00 12.00 10.92
## [3277] 12.00 13.71 10.00 10.33 12.73 13.33 12.22 11.33 11.00 13.80 12.00 11.25
## [3289] 10.50 11.56 14.00 13.00 11.00 13.68 12.10 10.50 11.94 12.86 14.25 0.00
## [3301] 0.00 13.89 13.47 13.60 14.67 13.67 13.30 13.45 13.42 0.00 11.33 16.00
## [3313] 11.00 12.86 0.00 14.80 13.00 0.00 10.00 11.20 11.83 0.00 10.50 12.50
## [3325] 0.00 11.00 12.33 0.00 17.00 11.00 11.14 12.17 11.00 11.00 13.25 0.00
## [3337] 12.50 12.14 12.00 11.25 0.00 12.40 12.83 13.00 12.00 12.00 0.00 0.00
## [3349] 11.38 12.00 11.83 12.00 12.00 12.71 15.30 11.50 13.00 0.00 0.00 11.00
## [3361] 12.67 13.50 12.00 0.00 11.80 11.50 11.50 14.62 14.06 11.00 0.00 12.19
## [3373] 12.83 12.88 12.17 13.43 14.50 12.14 11.25 13.90 13.77 11.62 15.17 0.00
## [3385] 14.50 10.80 14.00 13.29 12.75 10.50 12.71 12.89 13.00 12.20 12.80 13.79
## [3397] 0.00 14.50 14.35 11.50 11.71 13.57 13.00 13.57 10.20 0.00 12.20 14.15
## [3409] 0.00 13.83 13.43 12.45 11.00 0.00 13.27 13.55 12.17 11.00 13.29 13.33
## [3421] 13.26 0.00 12.67 14.60 0.00 12.33 10.80 11.67 12.50 0.00 15.33 14.20
## [3433] 14.83 13.64 13.83 11.83 13.43 10.50 11.42 12.75 11.15 11.67 11.50 13.83
## [3445] 11.71 11.68 15.71 0.00 13.00 14.49 12.29 13.38 11.57 12.66 10.00 13.71
## [3457] 13.07 15.33 11.57 0.00 12.90 13.13 11.50 10.33 13.50 0.00 12.00 11.14
## [3469] 11.40 12.77 13.80 13.33 0.00 11.36 0.00 15.69 15.05 11.50 11.00 13.00
## [3481] 12.94 0.00 0.00 13.00 12.18 11.33 13.00 0.00 12.50 11.00 0.00 0.00
## [3493] 0.00 0.00 12.40 15.50 11.50 13.33 12.67 0.00 12.60 13.50 13.00 11.71
## [3505] 12.17 0.00 0.00 11.50 11.25 12.29 12.72 12.40 0.00 14.00 11.67 13.00
## [3517] 0.00 0.00 11.50 11.71 12.60 11.64 14.88 10.00 14.20 12.71 11.60 11.94
## [3529] 11.60 12.70 13.33 13.33 13.40 0.00 11.00 12.00 0.00 0.00 12.50 13.67
## [3541] 10.00 11.50 12.25 13.60 10.50 13.27 12.51 0.00 0.00 13.48 12.56 0.00
## [3553] 13.00 16.50 13.17 13.80 11.17 0.00 12.67 12.60 13.06 13.83 0.00 16.00
## [3565] 0.00 10.67 14.50 14.00 13.33 0.00 12.00 16.20 10.29 0.00 13.57 14.29
## [3577] 10.20 10.25 0.00 14.83 13.62 12.27 0.00 12.50 13.22 15.00 0.00 13.17
## [3589] 13.83 0.00 0.00 13.15 12.33 13.00 11.50 13.25 13.33 13.50 12.67 15.09
## [3601] 0.00 13.17 12.83 11.80 11.83 12.80 11.80 0.00 15.80 0.00 12.50 14.67
## [3613] 12.50 12.00 13.14 12.67 15.00 13.60 12.50 13.33 12.25 15.10 13.17 11.00
## [3625] 11.67 10.00 11.57 12.17 0.00 13.83 12.36 12.17 12.00 12.42 12.75 14.93
## [3637] 13.00 12.86 14.46 14.00 13.50 0.00 11.67 12.00 11.71 12.67 11.75 0.00
## [3649] 12.33 11.67 13.25 11.83 13.30 12.56 12.83 12.83 12.67 13.27 12.40 14.50
## [3661] 0.00 14.29 12.33 12.58 13.73 12.88 14.62 0.00 12.67 12.49 13.67 16.00
## [3673] 14.14 11.83 12.67 12.50 10.89 13.00 15.17 12.67 0.00 12.00 0.00 0.00
## [3685] 11.00 15.71 10.82 12.00 12.60 13.00 11.60 10.00 14.00 12.60 0.00 11.33
## [3697] 12.67 10.80 12.88 0.00 12.83 12.60 0.00 0.00 14.17 13.40 11.20 0.00
## [3709] 12.67 12.33 12.25 0.00 10.75 0.00 0.00 14.33 11.50 0.00 10.50 13.50
## [3721] 11.00 10.00 0.00 12.00 12.25 11.40 0.00 14.25 14.45 14.54 12.73 13.20
## [3733] 0.00 12.33 11.20 13.20 11.83 11.33 13.60 0.00 12.86 14.33 13.50 14.43
## [3745] 0.00 0.00 12.83 0.00 0.00 14.67 13.94 14.70 11.67 14.85 12.00 13.69
## [3757] 12.40 13.40 11.80 0.00 11.77 0.00 13.29 11.67 11.50 13.08 12.67 11.33
## [3769] 13.60 13.17 0.00 11.67 13.50 0.00 13.17 12.50 13.38 13.17 13.40 13.00
## [3781] 13.15 12.83 12.14 13.34 13.00 12.00 0.00 11.00 11.50 13.33 14.59 11.00
## [3793] 0.00 0.00 12.00 14.00 13.57 0.00 14.25 0.00 0.00 13.54 13.11 12.67
## [3805] 10.75 10.75 13.67 13.83 13.18 12.75 12.86 12.00 11.67 16.50 12.33 12.59
## [3817] 11.50 11.89 0.00 0.00 13.00 0.00 15.17 11.75 0.00 0.00 11.33 12.60
## [3829] 0.00 15.50 12.37 13.20 11.43 0.00 14.00 12.00 0.00 10.00 10.00 0.00
## [3841] 11.17 11.75 11.75 10.00 14.00 0.00 12.00 0.00 11.89 13.83 0.00 11.40
## [3853] 0.00 10.64 11.00 16.83 13.57 14.71 0.00 10.00 11.00 11.00 12.00 11.12
## [3865] 11.33 12.00 0.00 14.54 12.17 13.50 14.75 12.38 12.73 12.50 0.00 0.00
## [3877] 13.44 14.20 13.55 11.60 13.57 13.83 11.25 10.20 15.68 10.83 14.50 10.40
## [3889] 13.00 12.24 13.00 14.17 14.25 12.00 13.25 13.18 11.00 11.97 12.40 12.60
## [3901] 13.90 11.50 14.20 10.67 0.00 11.00 13.96 12.50 13.33 0.00 11.67 15.71
## [3913] 11.00 12.25 12.20 13.00 12.00 13.33 13.00 12.91 11.00 13.58 12.40 12.89
## [3925] 11.55 10.00 14.34 14.14 0.00 11.80 13.33 14.50 12.67 10.00 0.00 11.00
## [3937] 12.00 10.00 14.21 14.31 11.00 0.00 12.00 0.00 0.00 13.86 0.00 0.00
## [3949] 11.00 13.20 13.50 0.00 14.21 13.00 12.00 0.00 12.80 13.60 13.97 15.00
## [3961] 0.00 15.08 13.38 13.25 11.71 13.01 10.67 0.00 13.00 12.00 12.17 11.85
## [3973] 11.00 12.33 12.00 14.43 13.78 13.80 14.86 13.00 12.14 15.67 12.50 12.83
## [3985] 0.00 12.50 11.25 15.25 14.00 12.08 14.62 10.50 12.83 12.50 11.23 10.50
## [3997] 12.00 10.99 12.62 13.00 0.00 0.00 13.50 13.52 13.17 0.00 13.12 14.40
## [4009] 12.00 0.00 0.00 10.80 0.00 16.13 14.84 10.33 12.00 0.00 13.17 13.95
## [4021] 11.33 12.75 12.60 12.25 0.00 11.00 11.83 13.07 13.83 13.83 11.80 13.33
## [4033] 13.75 0.00 0.00 0.00 13.33 10.00 15.67 11.86 14.50 12.17 12.60 12.29
## [4045] 12.67 0.00 12.86 13.90 13.82 13.31 0.00 12.17 11.25 12.40 14.67 12.00
## [4057] 14.00 12.57 15.54 0.00 15.00 12.25 15.69 12.29 11.83 12.17 11.89 0.00
## [4069] 11.80 11.17 14.06 11.75 13.17 13.50 12.62 0.00 13.97 11.00 12.80 13.57
## [4081] 0.00 11.50 11.25 13.71 0.00 12.00 12.67 13.29 10.38 12.00 11.40 13.25
## [4093] 13.86 12.17 13.75 15.43 13.83 11.83 0.00 0.00 12.33 11.17 14.67 11.20
## [4105] 13.71 12.80 13.25 13.78 15.11 11.00 15.80 13.78 12.16 0.00 14.33 11.83
## [4117] 14.83 14.20 12.20 13.00 12.49 17.00 10.80 14.72 13.50 11.97 12.00 12.33
## [4129] 15.31 12.67 14.37 12.08 12.25 12.20 11.00 12.80 11.86 12.29 12.33 11.25
## [4141] 0.00 16.00 11.67 12.40 10.74 0.00 12.00 12.75 10.00 13.42 15.17 13.83
## [4153] 13.33 0.00 11.67 15.00 13.24 13.00 13.07 13.50 11.80 12.60 12.17 12.17
## [4165] 0.00 13.56 12.25 14.33 10.50 0.00 12.75 0.00 14.00 14.09 13.33 12.07
## [4177] 12.67 12.12 13.20 14.15 13.50 0.00 12.20 14.80 11.00 0.00 14.00 11.83
## [4189] 11.75 12.33 11.67 12.67 12.25 11.29 11.50 11.67 13.51 13.00 15.00 12.74
## [4201] 11.75 12.17 0.00 13.40 11.80 13.53 14.17 14.65 0.00 13.60 12.83 14.67
## [4213] 13.33 13.40 13.31 0.00 0.00 12.33 13.50 13.00 12.50 17.00 13.50 12.71
## [4225] 13.00 12.57 11.50 13.50 13.60 12.00 14.95 11.25 10.67 14.99 10.50 11.25
## [4237] 12.33 13.02 11.33 16.14 14.83 13.33 11.00 11.71 12.33 0.00 11.92 11.83
## [4249] 12.33 14.30 11.83 10.00 12.00 12.20 11.33 13.85 12.41 12.67 12.55 13.00
## [4261] 0.00 12.22 13.29 11.67 13.56 13.17 0.00 11.67 11.00 13.00 13.67 14.60
## [4273] 12.51 14.00 13.17 13.00 13.00 10.00 14.33 0.00 11.00 11.25 10.75 11.00
## [4285] 10.86 11.75 12.80 12.33 11.33 11.60 10.92 0.00 13.63 10.33 13.74 11.62
## [4297] 11.50 14.00 11.33 10.00 11.71 0.00 10.77 11.60 13.75 11.00 0.00 0.00
## [4309] 0.00 12.33 13.43 0.00 14.75 12.48 0.00 11.67 12.00 12.00 15.25 12.40
## [4321] 12.33 11.50 12.20 10.50 14.40 12.85 12.00 0.00 13.67 11.86 0.00 0.00
## [4333] 13.20 12.71 12.50 10.67 17.00 13.00 12.67 13.29 11.67 14.24 13.00 14.06
## [4345] 11.83 12.83 10.00 11.00 14.11 12.47 11.83 12.50 11.67 0.00 10.33 16.17
## [4357] 12.67 10.50 11.50 13.00 11.97 13.35 12.00 10.50 11.50 0.00 13.57 14.70
## [4369] 0.00 11.83 0.00 13.18 0.00 13.00 13.74 0.00 12.22 11.07 13.43 11.40
## [4381] 11.32 0.00 15.00 13.17 11.00 0.00 12.33 12.25 11.92 14.33 12.00 13.76
## [4393] 11.25 12.33 14.89 12.17 12.67 12.60 13.00 13.88 10.75 14.67 12.60 12.41
## [4405] 11.00 14.31 12.00 12.83 11.40 14.60 13.50 12.50 13.00 11.60 11.80 12.33
## [4417] 12.62 13.83 12.50 13.60 12.00 14.91 13.80 11.67round(podatki$Curricular.units.2nd.sem..grade.,2)## [1] 0.00 13.67 0.00 12.40 13.00 11.50 14.35 0.00 14.14 13.50 14.20 13.21
## [13] 0.00 11.00 12.00 0.00 11.00 14.54 12.25 13.50 0.00 11.43 12.86 12.29
## [25] 14.11 11.00 13.29 13.00 12.33 13.72 10.57 13.40 13.50 14.38 13.43 10.00
## [37] 0.00 12.00 11.60 12.00 0.00 15.80 14.34 13.80 0.00 14.33 13.20 13.77
## [49] 13.29 12.83 14.17 11.83 11.00 15.80 11.00 13.60 0.00 12.90 14.94 0.00
## [61] 12.22 12.00 0.00 10.00 0.00 11.00 0.00 12.43 10.75 10.80 0.00 13.75
## [73] 0.00 12.00 12.33 10.86 11.00 13.33 15.06 11.67 12.20 0.00 13.30 11.33
## [85] 11.00 13.08 11.60 11.20 13.80 0.00 0.00 13.50 0.00 0.00 12.33 13.25
## [97] 13.33 14.48 13.80 0.00 13.40 0.00 0.00 14.23 0.00 12.27 0.00 13.25
## [109] 12.30 13.00 15.00 11.00 12.80 12.57 12.52 13.00 10.75 10.67 11.40 14.00
## [121] 11.00 11.25 0.00 14.20 12.20 0.00 13.78 13.40 13.67 15.01 13.74 13.00
## [133] 14.60 0.00 11.71 12.50 11.50 14.83 12.89 17.59 12.67 12.00 0.00 11.50
## [145] 12.33 10.80 0.00 11.67 14.17 14.18 0.00 13.40 10.83 11.80 10.00 11.50
## [157] 11.80 11.86 11.83 12.60 13.00 12.76 15.36 11.00 14.20 13.00 0.00 11.00
## [169] 14.26 11.33 10.50 13.56 11.68 12.00 13.17 13.50 12.00 11.95 10.40 14.58
## [181] 12.79 13.17 0.00 0.00 0.00 10.57 10.00 13.05 0.00 12.00 12.50 10.00
## [193] 0.00 0.00 12.24 0.00 12.93 0.00 14.43 11.33 14.33 11.33 12.32 11.71
## [205] 11.25 10.75 12.91 14.17 13.40 12.80 12.64 12.92 15.86 0.00 12.00 13.31
## [217] 11.60 0.00 0.00 13.50 12.33 14.50 12.50 12.19 14.91 15.80 13.80 12.86
## [229] 0.00 11.57 12.67 0.00 13.20 12.00 15.00 13.00 13.17 11.57 14.25 10.33
## [241] 11.46 13.56 13.60 0.00 12.36 13.22 13.15 11.33 12.25 14.14 12.40 12.83
## [253] 13.00 0.00 10.80 0.00 12.33 12.50 12.67 13.00 10.60 0.00 12.17 14.00
## [265] 12.00 11.67 14.83 12.80 12.50 13.67 12.80 13.00 12.33 13.55 15.43 15.39
## [277] 10.67 13.20 13.78 13.81 11.40 14.17 13.80 12.83 11.86 13.83 12.33 11.50
## [289] 11.50 13.38 14.50 13.83 13.00 11.67 11.33 14.73 13.67 12.33 13.14 12.86
## [301] 13.71 12.20 16.17 10.25 0.00 11.00 14.60 0.00 13.20 11.00 15.14 11.33
## [313] 11.80 13.67 0.00 16.40 14.88 14.36 11.86 13.08 0.00 13.06 14.06 12.00
## [325] 13.00 11.67 13.33 11.00 11.40 11.60 12.67 0.00 13.00 11.67 13.67 14.67
## [337] 14.57 13.39 12.43 12.50 12.00 0.00 12.86 13.10 12.00 12.50 12.31 11.67
## [349] 13.83 11.25 11.50 13.33 0.00 14.20 0.00 16.43 13.44 0.00 0.00 0.00
## [361] 11.83 10.00 11.00 13.71 13.98 15.75 14.03 11.20 13.67 13.41 13.57 10.83
## [373] 14.43 12.86 0.00 12.80 0.00 15.29 13.33 13.50 10.98 13.75 10.33 13.17
## [385] 11.11 11.17 12.33 12.00 12.40 14.17 11.00 12.14 11.40 12.33 14.00 12.86
## [397] 12.00 12.00 13.71 0.00 11.20 10.33 11.00 12.75 14.73 0.00 14.25 14.80
## [409] 14.57 0.00 14.65 12.40 14.07 15.60 11.83 15.40 12.38 11.00 11.60 0.00
## [421] 13.09 14.80 0.00 13.25 14.10 13.92 13.57 10.67 0.00 14.60 12.08 12.80
## [433] 12.40 0.00 14.57 13.81 10.50 13.67 0.00 11.30 16.00 12.00 12.30 12.69
## [445] 11.00 14.17 16.05 14.06 12.80 12.80 14.40 13.38 13.98 12.60 11.25 11.00
## [457] 0.00 12.00 14.09 13.33 14.60 13.45 10.50 12.20 10.40 10.80 12.62 13.27
## [469] 13.31 12.20 13.49 11.83 12.83 13.97 0.00 12.80 0.00 0.00 13.22 11.80
## [481] 14.04 14.31 0.00 13.00 12.13 12.20 10.57 11.75 14.48 13.54 11.88 13.33
## [493] 12.60 11.40 12.83 11.00 0.00 12.20 12.67 12.77 12.60 14.60 10.83 0.00
## [505] 11.72 12.53 13.80 13.67 14.00 0.00 0.00 0.00 11.75 0.00 0.00 0.00
## [517] 12.40 11.67 11.00 10.20 12.61 12.60 13.50 13.00 0.00 11.00 10.50 0.00
## [529] 0.00 11.75 11.67 0.00 11.69 0.00 0.00 11.29 0.00 12.40 13.17 11.33
## [541] 15.02 12.00 12.62 15.19 12.60 11.00 13.50 14.50 13.50 11.00 12.00 13.75
## [553] 13.67 0.00 0.00 10.86 12.00 0.00 10.67 12.51 12.00 12.67 11.33 13.20
## [565] 13.62 14.71 0.00 11.33 14.20 11.50 12.00 12.00 10.80 10.83 0.00 0.00
## [577] 13.83 10.20 11.67 13.62 0.00 12.61 13.29 12.80 11.60 15.20 13.20 12.29
## [589] 12.00 13.82 14.56 11.70 13.57 13.00 14.00 11.55 10.00 12.60 13.78 11.46
## [601] 0.00 11.60 15.74 12.33 15.81 0.00 0.00 12.36 0.00 11.98 12.57 14.17
## [613] 11.17 13.20 12.36 13.86 10.67 13.79 13.02 11.75 12.50 10.00 10.25 13.73
## [625] 12.67 10.80 11.33 13.81 14.17 12.00 12.04 13.00 15.50 11.70 14.00 12.71
## [637] 12.63 11.40 11.60 11.83 0.00 11.00 12.33 14.27 0.00 13.33 10.00 14.83
## [649] 13.21 10.75 16.43 13.50 12.61 11.50 11.00 10.00 10.00 11.45 12.40 0.00
## [661] 15.50 11.71 13.67 13.25 14.44 16.00 11.75 13.55 0.00 13.55 11.00 14.71
## [673] 11.74 13.20 13.50 11.00 15.00 12.00 0.00 0.00 10.67 14.00 14.00 0.00
## [685] 11.22 12.80 11.00 12.48 14.00 0.00 0.00 12.38 13.00 0.00 15.50 13.50
## [697] 13.67 10.80 11.71 17.00 12.00 13.67 12.50 0.00 14.86 13.33 12.14 14.23
## [709] 15.78 0.00 0.00 0.00 11.60 13.11 14.40 12.00 0.00 0.00 17.60 12.40
## [721] 12.00 12.00 0.00 0.00 0.00 16.58 14.38 0.00 0.00 11.20 12.00 11.67
## [733] 11.60 12.75 0.00 12.00 12.33 11.33 11.18 13.00 0.00 12.50 12.40 10.33
## [745] 15.00 0.00 11.00 11.43 0.00 13.94 13.33 14.67 13.11 0.00 12.17 0.00
## [757] 12.33 11.36 13.00 11.80 12.38 0.00 12.00 10.00 13.00 11.20 12.40 12.57
## [769] 13.86 14.00 15.14 0.00 13.29 12.17 12.20 12.00 15.62 12.70 14.33 13.83
## [781] 15.50 10.50 14.63 13.35 12.33 12.14 14.00 14.54 14.00 0.00 13.83 0.00
## [793] 12.43 13.60 12.17 14.17 13.22 12.95 13.67 12.75 12.00 0.00 12.20 14.00
## [805] 14.29 10.00 12.17 13.00 0.00 11.50 0.00 13.67 13.63 14.14 15.00 12.67
## [817] 11.50 12.83 13.16 12.83 11.60 0.00 13.20 13.29 11.50 14.00 13.17 15.33
## [829] 14.25 0.00 11.00 0.00 12.50 10.00 0.00 11.00 10.75 13.50 0.00 12.40
## [841] 0.00 14.00 0.00 14.02 10.80 0.00 12.00 10.25 12.71 14.11 12.82 11.25
## [853] 14.17 13.84 0.00 0.00 13.83 0.00 0.00 10.00 13.25 0.00 12.14 14.50
## [865] 13.50 15.06 0.00 0.00 12.80 0.00 12.50 13.00 11.58 11.58 14.50 12.23
## [877] 11.00 0.00 11.60 12.14 13.20 0.00 0.00 11.43 12.60 12.33 13.00 11.00
## [889] 15.35 11.25 14.67 0.00 14.43 0.00 12.46 13.00 13.00 12.55 11.00 14.00
## [901] 14.00 11.20 12.89 12.95 0.00 12.55 0.00 11.00 10.00 0.00 13.33 13.40
## [913] 11.00 12.00 0.00 13.67 0.00 0.00 15.00 12.33 10.40 11.50 12.25 10.50
## [925] 11.33 13.70 0.00 12.17 0.00 0.00 12.50 13.29 15.11 11.50 11.71 14.33
## [937] 10.00 13.43 12.25 11.00 12.40 12.29 0.00 0.00 16.08 12.67 12.83 0.00
## [949] 11.50 0.00 11.60 0.00 12.67 0.00 12.00 11.00 11.67 13.00 12.67 0.00
## [961] 11.50 13.64 13.20 12.50 10.20 12.40 0.00 0.00 0.00 10.50 14.75 0.00
## [973] 0.00 15.50 11.12 10.33 12.67 13.25 14.67 12.25 10.50 11.40 12.50 10.83
## [985] 16.00 13.71 15.80 0.00 10.00 13.50 16.33 14.80 11.00 13.50 14.60 14.33
## [997] 13.55 11.50 13.40 13.00 0.00 0.00 0.00 11.00 17.43 12.00 15.23 13.22
## [1009] 14.43 13.71 13.19 12.41 12.00 0.00 11.60 12.33 0.00 12.91 0.00 12.29
## [1021] 12.98 11.20 11.68 13.50 12.86 10.50 11.80 12.20 14.88 13.31 10.50 10.75
## [1033] 14.14 15.57 0.00 14.00 0.00 13.17 12.83 10.60 10.40 12.79 11.20 12.43
## [1045] 12.20 0.00 13.17 14.10 12.94 16.09 0.00 15.10 15.20 13.00 15.86 14.67
## [1057] 12.24 14.57 11.25 12.69 13.25 0.00 11.17 14.45 11.75 14.62 13.42 11.40
## [1069] 14.81 12.80 14.75 14.33 12.50 14.86 13.00 12.00 12.00 14.00 0.00 13.61
## [1081] 12.67 11.00 12.60 14.86 12.62 0.00 13.67 13.17 13.33 0.00 12.00 0.00
## [1093] 11.67 11.57 12.55 10.67 0.00 11.25 12.83 14.07 13.20 0.00 10.25 10.57
## [1105] 11.60 0.00 14.90 12.45 10.60 12.67 12.67 13.33 12.50 11.33 14.05 13.12
## [1117] 0.00 13.57 11.70 12.33 16.40 13.20 13.49 13.00 13.50 13.00 16.58 11.00
## [1129] 13.60 12.11 13.06 13.29 10.67 15.16 0.00 11.00 13.62 11.67 13.30 14.25
## [1141] 12.83 11.00 13.75 12.57 12.62 12.20 0.00 11.40 12.17 13.49 11.29 0.00
## [1153] 14.43 13.76 13.26 12.00 10.00 12.50 11.83 13.29 11.80 12.64 14.65 11.33
## [1165] 0.00 14.75 11.14 13.00 13.86 11.75 13.20 15.07 12.00 12.67 12.60 11.25
## [1177] 12.17 14.20 10.00 12.51 12.33 10.50 11.90 13.20 11.93 12.29 12.97 11.00
## [1189] 11.50 13.14 0.00 12.04 0.00 14.58 15.31 12.71 0.00 10.33 15.17 16.38
## [1201] 14.71 12.17 14.80 11.75 0.00 13.62 12.33 12.90 0.00 10.50 0.00 11.50
## [1213] 13.63 11.50 12.23 16.38 12.00 13.29 12.76 12.17 0.00 15.68 0.00 12.50
## [1225] 13.58 15.83 11.60 12.00 13.76 12.20 12.20 11.67 14.36 12.67 13.93 11.00
## [1237] 13.74 0.00 13.20 0.00 11.00 11.67 10.00 13.00 10.00 13.00 12.83 0.00
## [1249] 11.00 11.80 16.00 12.86 12.33 11.33 14.75 10.00 12.86 13.80 13.60 15.88
## [1261] 11.50 14.00 0.00 16.20 11.79 13.42 14.17 12.46 12.60 0.00 12.43 12.40
## [1273] 12.00 0.00 12.33 13.50 12.67 11.80 11.50 12.62 13.00 13.02 0.00 18.57
## [1285] 11.50 12.50 13.80 11.83 11.50 13.77 13.62 14.29 10.00 17.60 0.00 0.00
## [1297] 0.00 12.38 11.80 12.00 0.00 0.00 0.00 13.33 15.00 12.83 13.30 12.20
## [1309] 13.31 11.99 12.89 13.88 12.83 13.41 12.00 14.65 11.75 10.67 11.00 11.20
## [1321] 12.33 14.00 13.76 12.80 12.00 14.33 12.67 0.00 14.62 13.75 13.91 13.99
## [1333] 12.00 12.00 13.33 10.40 11.69 12.00 11.00 11.40 11.33 12.20 15.00 13.50
## [1345] 11.00 13.33 13.50 12.50 13.33 12.83 0.00 15.66 11.33 0.00 11.17 12.67
## [1357] 0.00 0.00 0.00 0.00 0.00 13.33 0.00 0.00 13.70 0.00 13.88 12.20
## [1369] 11.00 12.86 14.00 15.03 11.71 12.40 11.33 0.00 12.50 0.00 0.00 0.00
## [1381] 12.58 0.00 11.08 13.35 16.00 0.00 0.00 11.83 0.00 10.60 13.88 12.60
## [1393] 0.00 13.67 12.50 11.33 13.00 13.78 12.23 14.14 0.00 12.40 13.80 15.07
## [1405] 0.00 0.00 12.34 10.80 11.00 11.60 0.00 12.00 11.70 11.67 14.51 12.33
## [1417] 0.00 13.60 11.80 12.83 11.40 12.67 11.83 11.50 13.40 0.00 11.50 13.50
## [1429] 12.25 12.83 12.91 10.00 11.00 15.83 12.88 14.00 11.00 12.17 14.33 12.57
## [1441] 14.25 12.06 14.67 0.00 13.83 0.00 0.00 12.33 13.67 12.56 12.17 12.31
## [1453] 0.00 11.17 12.25 0.00 13.00 12.04 10.00 0.00 12.50 12.30 12.00 10.00
## [1465] 10.40 12.75 0.00 14.25 14.17 13.67 11.40 11.50 12.29 0.00 12.50 12.60
## [1477] 11.50 13.00 0.00 0.00 14.80 11.33 14.43 13.40 10.98 11.50 14.29 12.20
## [1489] 0.00 14.83 13.50 11.00 10.50 13.00 0.00 14.14 14.69 13.00 12.33 12.60
## [1501] 13.86 0.00 13.83 10.84 12.46 12.00 10.50 0.00 13.00 0.00 0.00 12.50
## [1513] 0.00 14.33 0.00 14.89 0.00 13.58 0.00 0.00 0.00 15.20 0.00 11.00
## [1525] 0.00 12.83 12.60 12.40 13.25 11.33 13.00 13.03 11.75 16.20 13.60 12.50
## [1537] 0.00 12.00 11.67 0.00 10.80 0.00 0.00 0.00 12.00 12.50 11.80 0.00
## [1549] 0.00 0.00 12.00 10.67 10.92 13.00 14.33 14.23 0.00 0.00 0.00 13.25
## [1561] 12.75 14.25 12.40 11.00 14.00 12.17 15.61 11.40 11.67 0.00 13.86 0.00
## [1573] 0.00 11.75 12.40 0.00 13.75 13.00 12.00 0.00 14.17 11.00 11.00 11.20
## [1585] 13.00 0.00 12.25 10.80 12.00 12.17 0.00 0.00 10.33 0.00 11.75 11.00
## [1597] 12.50 16.14 11.80 11.33 0.00 14.25 10.33 13.60 0.00 11.62 13.00 12.89
## [1609] 13.60 12.57 12.50 12.40 12.28 0.00 11.50 11.00 14.50 11.80 13.00 11.80
## [1621] 14.50 13.00 11.25 11.75 10.44 0.00 12.78 11.00 12.75 0.00 11.75 0.00
## [1633] 14.20 12.82 11.80 13.33 13.00 11.65 0.00 14.82 12.91 14.86 14.66 11.00
## [1645] 11.00 0.00 14.50 14.39 12.14 14.36 14.51 14.70 14.00 15.06 0.00 12.60
## [1657] 13.00 10.50 0.00 0.00 14.14 15.67 15.74 15.07 11.75 15.00 12.33 13.76
## [1669] 10.00 13.00 11.00 14.00 12.00 14.08 12.77 0.00 0.00 12.60 13.40 0.00
## [1681] 14.00 12.67 11.60 12.75 13.00 15.00 12.29 0.00 0.00 0.00 0.00 0.00
## [1693] 14.02 12.40 0.00 13.29 12.17 0.00 0.00 0.00 15.63 14.50 0.00 11.50
## [1705] 13.00 11.00 0.00 12.25 13.12 12.45 12.00 13.38 11.34 11.50 12.17 13.34
## [1717] 13.03 10.00 14.50 0.00 12.14 11.40 15.43 12.40 12.67 12.00 13.36 10.75
## [1729] 0.00 12.85 12.80 12.00 12.50 11.00 11.43 13.12 13.05 13.75 13.83 0.00
## [1741] 12.67 12.00 13.33 10.00 0.00 10.00 11.50 0.00 0.00 12.40 12.25 0.00
## [1753] 12.00 10.50 0.00 14.20 12.27 0.00 15.00 12.60 11.83 0.00 16.50 11.25
## [1765] 12.60 0.00 14.00 13.67 0.00 10.33 12.00 10.00 14.43 12.00 10.00 0.00
## [1777] 11.43 12.00 11.00 14.50 12.25 11.17 15.57 12.00 15.91 11.50 0.00 13.75
## [1789] 0.00 11.33 13.08 0.00 13.50 0.00 12.33 13.51 12.17 11.67 13.33 0.00
## [1801] 12.29 13.29 12.80 11.14 0.00 0.00 11.50 0.00 12.00 13.00 12.83 13.54
## [1813] 12.60 11.50 0.00 13.73 12.00 12.50 0.00 14.75 11.67 11.10 0.00 10.50
## [1825] 12.67 14.17 14.33 10.50 0.00 12.00 11.50 14.00 11.60 12.29 14.86 11.50
## [1837] 12.14 12.16 13.43 15.50 0.00 0.00 11.00 11.40 12.36 13.00 12.25 10.00
## [1849] 12.69 11.00 0.00 14.80 11.80 14.67 10.50 0.00 12.88 12.40 12.33 12.50
## [1861] 0.00 11.00 0.00 13.17 0.00 12.40 0.00 0.00 14.33 12.67 0.00 0.00
## [1873] 15.01 0.00 12.75 13.30 0.00 0.00 0.00 13.56 14.64 10.33 0.00 0.00
## [1885] 11.72 12.18 11.00 0.00 14.33 0.00 0.00 13.44 0.00 0.00 12.18 11.00
## [1897] 11.50 11.50 0.00 14.00 12.67 12.56 14.00 13.12 11.67 14.17 15.66 12.94
## [1909] 11.00 14.27 14.00 12.48 15.31 0.00 12.20 13.45 12.60 12.94 12.80 14.60
## [1921] 13.50 14.00 10.00 12.50 0.00 14.00 12.71 12.50 13.00 15.11 13.22 12.33
## [1933] 11.25 13.37 12.83 13.89 12.80 13.68 12.00 11.20 12.17 13.17 14.50 11.40
## [1945] 13.14 14.96 14.04 14.00 13.33 12.33 0.00 0.00 0.00 12.00 12.46 13.17
## [1957] 11.50 14.81 11.71 13.00 12.67 0.00 13.80 13.71 10.33 13.46 13.00 11.60
## [1969] 10.67 15.40 11.00 12.14 13.12 12.20 13.24 11.40 12.62 12.50 13.00 14.50
## [1981] 13.00 11.83 13.29 13.97 14.14 11.75 14.66 0.00 12.67 12.20 12.80 0.00
## [1993] 11.75 11.80 0.00 11.67 13.10 13.33 0.00 11.38 10.33 0.00 12.60 12.00
## [2005] 0.00 13.20 14.17 12.00 0.00 0.00 12.67 12.40 10.60 0.00 0.00 13.29
## [2017] 12.20 14.22 13.00 13.83 0.00 0.00 0.00 12.29 11.75 12.91 0.00 0.00
## [2029] 12.97 13.67 14.37 0.00 12.25 0.00 14.17 14.38 10.00 12.00 11.50 11.67
## [2041] 11.00 11.60 13.50 12.17 12.80 12.84 0.00 11.22 15.12 13.44 10.83 12.29
## [2053] 0.00 13.07 14.06 13.50 12.64 12.00 11.25 12.00 13.67 13.39 13.33 11.00
## [2065] 13.20 15.00 12.67 12.50 11.00 12.33 11.78 12.92 13.80 13.80 13.67 15.00
## [2077] 12.33 14.38 13.04 14.15 12.47 14.15 14.05 14.67 13.17 0.00 0.00 15.17
## [2089] 12.63 12.60 14.23 11.33 15.70 15.20 15.60 12.86 0.00 12.00 13.78 11.67
## [2101] 11.83 12.00 14.29 10.67 14.43 13.40 12.50 13.20 11.80 13.00 15.33 14.33
## [2113] 16.80 11.86 11.25 0.00 12.00 12.83 14.40 0.00 0.00 12.40 11.60 0.00
## [2125] 0.00 10.00 13.74 12.76 0.00 13.25 12.75 12.00 12.20 13.05 13.61 0.00
## [2137] 12.17 12.50 14.44 11.50 12.73 11.29 13.29 0.00 13.67 14.17 12.83 12.50
## [2149] 14.80 14.43 13.29 12.33 13.13 13.00 15.14 15.09 0.00 13.14 14.33 10.33
## [2161] 14.57 10.75 0.00 13.78 15.33 13.83 14.96 11.20 12.80 17.17 13.71 12.17
## [2173] 11.00 0.00 12.75 0.00 14.17 10.50 14.77 12.71 0.00 10.50 13.06 12.90
## [2185] 10.50 12.33 11.14 13.40 12.67 12.33 0.00 0.00 16.00 11.00 0.00 12.29
## [2197] 12.25 10.33 10.00 0.00 0.00 12.60 12.50 0.00 11.80 14.12 0.00 13.33
## [2209] 10.57 0.00 13.10 13.17 12.00 13.00 15.17 11.00 13.60 11.00 13.50 14.67
## [2221] 12.74 13.13 11.67 0.00 14.94 10.00 13.00 0.00 14.00 10.75 0.00 0.00
## [2233] 0.00 11.67 12.00 0.00 13.00 0.00 11.33 0.00 12.20 11.33 10.50 13.91
## [2245] 10.00 13.67 12.42 0.00 0.00 13.25 14.00 12.25 14.40 0.00 0.00 14.33
## [2257] 12.25 11.50 12.67 13.17 12.71 11.50 0.00 15.00 11.80 14.80 13.00 0.00
## [2269] 10.67 0.00 0.00 12.80 11.14 0.00 0.00 10.50 14.43 12.75 11.00 0.00
## [2281] 12.31 10.50 10.00 11.80 11.50 0.00 13.40 14.43 11.50 0.00 13.50 11.00
## [2293] 11.33 13.33 0.00 13.43 10.00 11.00 11.00 0.00 14.00 10.80 11.00 14.71
## [2305] 0.00 12.17 0.00 0.00 0.00 14.20 14.00 12.49 0.00 14.60 12.17 15.60
## [2317] 16.00 0.00 0.00 14.71 0.00 16.50 13.00 14.09 10.50 0.00 10.00 10.67
## [2329] 0.00 0.00 0.00 0.00 12.40 0.00 14.33 11.17 11.20 0.00 13.33 13.71
## [2341] 0.00 14.67 11.50 13.00 11.51 13.75 13.25 15.29 0.00 11.50 13.61 14.30
## [2353] 14.20 11.80 0.00 14.29 0.00 11.88 14.60 10.50 11.00 0.00 12.80 11.67
## [2365] 12.50 14.50 11.91 13.67 13.80 13.33 11.78 0.00 0.00 12.00 12.00 11.00
## [2377] 14.75 0.00 11.33 12.50 12.86 12.33 15.14 11.44 0.00 11.33 10.67 0.00
## [2389] 12.50 0.00 12.00 11.60 12.33 0.00 11.50 12.33 0.00 12.40 14.57 11.71
## [2401] 11.00 12.80 11.00 15.89 11.58 14.17 0.00 0.00 0.00 11.00 0.00 0.00
## [2413] 12.50 10.67 11.18 0.00 11.25 11.36 12.67 13.40 0.00 0.00 12.20 0.00
## [2425] 0.00 0.00 0.00 11.60 10.86 13.00 12.60 16.00 12.67 13.00 11.67 12.60
## [2437] 12.08 12.50 12.70 0.00 0.00 11.00 10.00 17.69 0.00 12.60 16.20 10.00
## [2449] 0.00 12.80 0.00 0.00 12.00 13.08 0.00 15.30 13.50 13.00 0.00 13.20
## [2461] 0.00 0.00 0.00 0.00 11.80 0.00 16.00 12.30 12.67 0.00 11.00 0.00
## [2473] 10.33 0.00 15.00 0.00 13.50 12.20 11.35 11.33 0.00 12.40 14.83 12.18
## [2485] 14.80 12.00 0.00 0.00 12.50 12.50 10.25 13.50 10.43 12.50 14.00 13.67
## [2497] 0.00 12.50 0.00 15.00 13.38 13.33 11.64 13.07 0.00 13.59 11.43 12.00
## [2509] 0.00 13.62 0.00 12.42 13.06 12.00 12.80 10.00 12.00 12.21 13.00 13.50
## [2521] 13.00 11.17 13.09 0.00 0.00 11.00 12.83 13.66 14.29 12.62 12.33 13.20
## [2533] 11.00 13.00 13.14 10.75 15.14 15.83 13.00 12.40 0.00 0.00 14.75 0.00
## [2545] 11.50 14.33 11.83 13.23 14.17 0.00 12.27 14.33 11.50 0.00 11.33 10.50
## [2557] 11.40 0.00 10.67 13.50 12.60 13.07 0.00 0.00 13.33 13.43 14.79 11.20
## [2569] 12.20 14.67 14.40 16.39 14.17 14.98 13.00 14.14 11.00 10.00 13.98 12.83
## [2581] 13.00 0.00 15.40 11.25 13.67 12.00 12.67 11.00 10.50 12.20 0.00 13.17
## [2593] 11.62 11.68 12.00 12.17 12.20 0.00 12.00 12.00 12.80 11.33 12.83 0.00
## [2605] 13.00 12.00 12.20 13.14 12.75 10.00 13.76 12.25 15.83 0.00 13.00 13.00
## [2617] 0.00 12.80 12.40 12.57 11.90 11.83 12.60 11.00 12.00 12.00 14.39 12.20
## [2629] 11.75 14.33 12.00 0.00 12.55 12.67 13.00 0.00 0.00 0.00 12.20 12.12
## [2641] 0.00 11.50 0.00 13.50 13.83 0.00 12.14 12.00 13.50 12.00 13.22 11.00
## [2653] 14.17 0.00 13.87 12.68 0.00 12.50 0.00 12.20 11.33 14.17 11.57 0.00
## [2665] 14.17 12.25 13.12 11.00 11.64 0.00 11.29 13.67 11.00 12.50 11.56 11.25
## [2677] 13.15 15.40 0.00 16.80 12.53 0.00 10.00 10.67 0.00 12.00 10.00 0.00
## [2689] 0.00 0.00 11.00 13.50 11.60 15.17 11.50 13.50 0.00 13.40 12.75 13.40
## [2701] 0.00 0.00 0.00 11.20 0.00 14.00 13.40 0.00 14.12 12.04 15.67 0.00
## [2713] 0.00 12.80 16.67 13.21 0.00 14.00 14.12 13.11 13.71 11.75 13.67 12.00
## [2725] 12.41 10.50 13.43 14.31 14.50 13.40 13.71 12.14 14.01 13.33 13.60 15.40
## [2737] 15.93 11.00 12.00 13.60 12.38 12.00 14.50 14.57 11.00 13.14 11.81 0.00
## [2749] 0.00 11.60 0.00 13.50 0.00 12.80 13.60 11.89 10.00 0.00 0.00 12.00
## [2761] 13.31 10.83 11.67 13.29 11.25 13.11 14.41 0.00 12.20 10.00 13.31 13.04
## [2773] 12.86 14.25 11.24 15.08 0.00 12.60 13.21 11.80 13.12 11.00 11.00 12.67
## [2785] 12.38 13.43 12.00 11.00 0.00 0.00 11.00 14.14 11.57 0.00 0.00 12.69
## [2797] 0.00 14.00 13.07 11.00 16.00 0.00 15.17 15.33 11.67 12.42 12.00 14.14
## [2809] 12.67 12.12 12.83 12.56 14.23 11.25 0.00 11.71 14.27 13.86 12.43 11.00
## [2821] 12.77 0.00 13.57 14.60 13.70 13.75 13.40 10.00 12.83 0.00 11.60 11.00
## [2833] 12.83 11.00 13.60 13.18 0.00 12.20 0.00 15.50 11.33 11.38 12.86 0.00
## [2845] 11.00 12.71 0.00 0.00 11.10 13.00 0.00 14.17 10.73 14.38 0.00 12.24
## [2857] 13.33 0.00 12.80 12.50 13.75 11.60 11.83 12.11 11.00 16.60 0.00 14.75
## [2869] 13.00 14.40 11.50 0.00 11.33 12.38 0.00 11.67 0.00 11.50 11.88 11.67
## [2881] 11.25 11.20 12.00 11.50 15.23 13.50 13.20 12.83 11.86 13.80 12.50 0.00
## [2893] 12.43 12.00 13.00 10.50 12.00 14.57 12.41 0.00 11.44 0.00 13.12 13.50
## [2905] 12.00 12.50 11.33 14.07 13.57 12.25 0.00 13.28 0.00 14.75 0.00 11.80
## [2917] 14.50 12.32 11.83 0.00 0.00 0.00 12.40 0.00 12.76 14.67 14.57 10.40
## [2929] 0.00 13.67 12.50 0.00 0.00 11.97 0.00 12.25 0.00 0.00 10.75 0.00
## [2941] 12.33 12.30 13.58 13.83 12.75 13.00 0.00 13.14 12.00 12.00 12.60 13.83
## [2953] 12.33 0.00 14.80 0.00 0.00 11.00 11.00 12.83 12.67 14.14 11.00 11.50
## [2965] 12.50 12.60 14.19 0.00 11.17 14.20 12.60 12.67 13.00 12.33 0.00 14.60
## [2977] 12.17 13.88 12.00 12.75 12.17 13.12 14.57 13.67 14.35 13.50 11.50 11.83
## [2989] 13.25 11.20 13.00 11.82 0.00 12.67 11.86 14.90 13.80 11.50 13.67 0.00
## [3001] 12.71 12.19 12.20 13.38 13.00 14.96 11.00 11.75 14.60 14.46 13.00 14.00
## [3013] 13.57 13.50 0.00 14.63 13.70 14.53 12.80 11.33 12.83 14.72 12.25 0.00
## [3025] 0.00 14.00 12.57 11.33 14.00 10.00 11.91 15.90 12.21 13.33 11.86 10.83
## [3037] 0.00 13.00 13.83 11.83 13.14 12.76 13.60 11.62 12.83 10.75 10.25 14.20
## [3049] 13.60 13.14 11.70 10.86 16.00 13.00 14.57 13.00 14.00 0.00 12.63 14.23
## [3061] 14.00 0.00 11.00 13.00 11.50 0.00 12.75 11.90 12.50 0.00 10.57 0.00
## [3073] 12.00 13.67 12.22 11.60 13.67 0.00 12.25 13.50 14.17 12.57 12.08 0.00
## [3085] 11.50 12.00 12.43 12.00 15.94 0.00 10.71 12.83 12.50 14.57 0.00 11.43
## [3097] 12.33 0.00 11.67 0.00 13.33 12.80 11.50 0.00 12.43 15.40 12.32 14.76
## [3109] 12.50 15.40 0.00 15.37 12.33 12.38 11.50 13.33 0.00 13.33 11.50 13.33
## [3121] 12.83 11.55 11.75 14.65 14.86 12.07 11.67 15.40 13.00 12.83 12.00 12.79
## [3133] 13.33 13.84 13.20 0.00 11.75 16.50 15.00 11.50 14.29 11.60 0.00 15.11
## [3145] 14.29 12.00 11.33 11.77 10.75 10.75 13.00 0.00 13.83 15.00 11.78 11.33
## [3157] 11.25 10.00 14.67 11.33 0.00 11.80 14.33 16.33 12.40 13.25 10.00 10.50
## [3169] 11.33 10.87 12.80 10.75 12.25 12.16 10.83 0.00 14.00 13.00 14.54 11.20
## [3181] 13.67 12.67 11.14 11.00 13.67 0.00 0.00 0.00 0.00 0.00 0.00 13.00
## [3193] 11.00 11.25 12.56 0.00 12.14 12.67 0.00 12.84 0.00 12.83 12.00 11.00
## [3205] 0.00 0.00 13.33 11.57 11.00 10.75 15.57 0.00 12.17 0.00 15.17 12.33
## [3217] 10.00 12.25 11.57 0.00 0.00 12.00 14.71 0.00 12.25 13.81 12.88 12.20
## [3229] 13.04 13.12 14.99 11.50 12.60 0.00 13.66 14.27 12.60 12.00 13.94 12.50
## [3241] 10.40 12.27 12.00 14.11 10.67 12.00 13.50 13.50 11.40 14.00 0.00 11.00
## [3253] 0.00 13.00 12.25 11.25 12.77 12.67 13.40 14.32 12.00 12.60 0.00 13.80
## [3265] 11.00 12.33 14.00 11.80 0.00 11.60 10.50 11.71 13.40 12.00 0.00 11.14
## [3277] 11.00 14.40 13.00 11.50 14.62 12.88 11.60 10.83 12.00 13.80 0.00 10.17
## [3289] 12.00 11.62 0.00 0.00 11.00 13.68 12.62 11.25 12.80 11.57 14.00 0.00
## [3301] 0.00 14.36 13.31 14.60 13.83 13.00 13.73 12.43 13.42 0.00 13.00 14.62
## [3313] 10.17 12.40 0.00 14.20 14.00 0.00 10.00 12.00 13.00 0.00 0.00 13.57
## [3325] 0.00 10.00 12.00 10.00 11.00 11.43 11.57 12.00 11.50 10.67 11.80 10.00
## [3337] 0.00 12.25 11.33 10.43 0.00 13.00 12.67 10.00 11.67 13.00 0.00 0.00
## [3349] 11.60 0.00 11.67 10.50 11.00 11.83 15.30 0.00 12.60 0.00 0.00 12.00
## [3361] 13.12 14.00 11.40 0.00 10.50 13.00 12.00 14.62 14.06 11.33 0.00 12.19
## [3373] 12.33 11.83 12.50 12.86 14.67 12.86 11.71 13.90 12.07 12.55 14.14 0.00
## [3385] 11.33 10.71 14.96 11.80 13.25 12.40 12.29 12.89 12.67 11.20 14.50 13.89
## [3397] 13.25 14.50 14.35 12.33 14.67 13.60 13.67 14.03 11.25 0.00 11.80 14.15
## [3409] 0.00 12.83 14.00 12.45 0.00 0.00 12.94 14.78 12.50 0.00 14.43 14.00
## [3421] 13.26 0.00 11.50 15.40 0.00 0.00 11.00 11.33 14.33 0.00 14.17 14.20
## [3433] 14.67 14.39 14.00 13.00 13.50 10.33 11.96 11.00 12.81 13.62 12.40 12.67
## [3445] 11.33 13.04 14.67 0.00 13.00 14.59 12.12 13.50 11.57 12.66 10.00 13.17
## [3457] 13.00 14.00 12.14 0.00 12.90 13.13 11.67 11.80 13.43 0.00 11.50 11.38
## [3469] 10.25 12.77 13.80 13.50 0.00 12.85 0.00 14.43 14.54 12.40 10.00 13.17
## [3481] 12.94 0.00 0.00 12.88 11.81 11.40 13.00 0.00 12.33 12.17 0.00 0.00
## [3493] 10.00 0.00 10.75 14.10 10.80 11.60 13.50 0.00 13.60 0.00 13.00 11.75
## [3505] 13.00 0.00 0.00 11.60 12.25 12.38 12.81 15.00 0.00 0.00 11.25 11.25
## [3517] 0.00 12.00 12.50 11.50 13.71 11.25 13.43 10.33 14.60 13.50 11.20 12.20
## [3529] 14.20 13.47 13.80 13.11 15.00 0.00 0.00 11.33 0.00 0.00 10.25 12.17
## [3541] 0.00 13.00 12.75 13.67 11.33 13.27 14.19 0.00 0.00 13.48 12.16 0.00
## [3553] 11.67 17.71 13.20 13.14 11.80 0.00 12.14 14.50 0.00 13.62 0.00 16.00
## [3565] 0.00 10.67 14.50 13.80 13.57 0.00 11.20 16.00 10.60 0.00 13.17 14.86
## [3577] 10.50 10.25 0.00 14.83 12.60 13.66 0.00 10.50 13.14 11.50 0.00 13.00
## [3589] 14.00 0.00 0.00 13.15 13.17 11.80 11.40 12.00 12.75 12.17 12.80 14.50
## [3601] 0.00 12.67 12.83 12.00 12.17 12.75 11.00 0.00 14.57 0.00 11.60 13.86
## [3613] 12.00 10.50 11.83 11.14 14.20 11.80 13.83 13.50 11.00 16.09 16.00 0.00
## [3625] 11.75 13.00 11.00 11.20 0.00 14.29 13.00 10.33 12.50 13.00 12.75 14.93
## [3637] 11.67 12.67 13.91 13.29 12.67 0.00 14.00 13.33 11.83 12.43 12.80 0.00
## [3649] 12.33 10.00 12.73 13.25 15.12 11.80 12.17 12.83 13.00 14.47 12.83 11.25
## [3661] 0.00 13.25 12.60 12.67 13.77 12.14 13.40 0.00 12.67 12.49 14.17 14.50
## [3673] 13.00 13.75 13.00 12.67 11.25 0.00 16.00 12.00 0.00 10.20 0.00 0.00
## [3685] 11.50 15.90 11.64 0.00 11.25 14.00 10.75 11.00 0.00 12.50 0.00 12.00
## [3697] 11.40 10.50 11.86 0.00 11.40 12.83 0.00 0.00 14.00 13.25 11.25 0.00
## [3709] 11.80 11.25 12.00 0.00 10.33 0.00 0.00 12.50 11.50 0.00 0.00 0.00
## [3721] 0.00 0.00 0.00 10.67 12.20 11.67 0.00 14.00 14.20 14.46 11.95 13.50
## [3733] 0.00 12.75 11.25 13.20 14.00 11.50 14.60 11.50 13.67 12.43 14.00 15.60
## [3745] 0.00 0.00 12.83 13.75 0.00 13.17 13.94 14.58 12.20 14.85 0.00 15.62
## [3757] 11.60 13.54 12.00 0.00 11.93 0.00 13.00 11.17 12.20 13.15 13.00 0.00
## [3769] 11.60 13.20 0.00 12.60 13.43 0.00 14.14 12.50 13.00 12.67 13.50 11.67
## [3781] 13.15 12.83 13.14 12.39 13.75 11.67 0.00 0.00 11.33 12.50 13.47 10.67
## [3793] 0.00 0.00 12.00 13.20 11.80 0.00 13.86 0.00 0.00 13.54 11.71 12.14
## [3805] 10.00 10.00 13.33 12.83 13.00 12.60 12.86 12.00 12.56 16.91 11.78 12.82
## [3817] 11.00 12.92 0.00 0.00 11.50 0.00 14.83 13.50 15.00 0.00 14.75 13.20
## [3829] 14.00 15.50 12.37 13.25 11.86 0.00 12.33 11.80 12.00 11.33 10.00 0.00
## [3841] 11.67 11.33 0.00 11.00 12.80 0.00 0.00 0.00 11.60 13.67 0.00 12.40
## [3853] 11.00 10.67 0.00 16.67 13.20 14.38 0.00 11.00 11.75 0.00 12.83 11.86
## [3865] 11.50 0.00 0.00 14.54 13.00 11.67 14.33 11.67 12.73 0.00 0.00 0.00
## [3877] 13.77 14.20 13.55 11.17 15.29 15.00 10.86 11.25 15.68 12.00 15.00 10.75
## [3889] 13.33 14.12 12.50 13.43 12.50 10.50 13.82 13.18 0.00 12.65 12.80 11.25
## [3901] 13.90 11.00 11.86 10.67 0.00 11.33 13.96 13.67 15.29 0.00 11.60 15.50
## [3913] 11.40 12.75 12.22 14.00 13.00 12.33 13.00 12.91 11.00 12.94 12.50 13.00
## [3925] 11.70 0.00 14.34 12.00 0.00 11.25 14.17 12.86 13.40 10.00 0.00 12.50
## [3937] 11.00 13.50 15.13 15.01 13.38 0.00 11.00 0.00 0.00 14.29 0.00 0.00
## [3949] 13.00 14.40 15.33 0.00 14.21 12.40 10.00 0.00 12.60 12.20 15.75 14.86
## [3961] 0.00 15.02 13.38 13.09 10.67 13.01 12.00 0.00 12.67 11.40 13.80 13.65
## [3973] 11.20 11.74 13.43 14.51 12.61 13.80 15.14 12.60 13.33 14.83 12.17 13.17
## [3985] 0.00 12.67 13.00 15.25 12.00 12.09 14.89 10.50 12.17 11.80 12.78 0.00
## [3997] 12.00 12.30 14.17 14.21 0.00 0.00 13.33 13.52 13.29 0.00 13.00 0.00
## [4009] 0.00 0.00 0.00 10.50 0.00 15.52 14.80 12.00 11.25 0.00 14.00 13.95
## [4021] 0.00 12.29 11.25 12.25 11.67 11.40 12.70 13.07 13.88 0.00 13.20 12.82
## [4033] 13.75 0.00 0.00 0.00 14.50 11.40 15.29 11.86 13.60 13.71 12.00 12.29
## [4045] 13.00 0.00 13.00 13.90 13.82 12.88 0.00 12.17 11.33 12.75 14.57 12.00
## [4057] 12.67 13.67 12.62 0.00 14.83 13.29 15.56 12.75 11.25 14.00 11.96 0.00
## [4069] 12.60 11.67 14.60 10.00 13.00 14.00 13.06 0.00 13.97 0.00 15.33 12.80
## [4081] 0.00 11.00 12.00 13.14 0.00 14.67 13.33 13.29 10.44 13.00 11.17 12.60
## [4093] 0.00 12.14 14.50 15.43 15.50 11.36 0.00 0.00 12.62 12.17 12.43 11.75
## [4105] 14.17 11.44 11.80 13.78 15.11 11.20 15.80 15.60 12.16 0.00 15.50 13.33
## [4117] 12.50 14.20 13.20 13.67 12.49 16.29 10.17 14.72 11.40 11.97 13.50 11.67
## [4129] 13.88 12.67 14.45 12.08 12.20 11.60 11.50 11.00 11.86 13.00 13.50 11.40
## [4141] 0.00 16.00 11.00 12.15 11.84 0.00 12.56 10.00 11.00 13.42 14.86 12.50
## [4153] 14.80 0.00 10.67 13.43 13.24 12.50 12.05 13.67 12.33 11.80 11.00 11.00
## [4165] 0.00 13.20 11.80 13.50 11.75 0.00 11.33 11.00 14.00 15.00 13.17 12.07
## [4177] 12.50 12.00 13.26 14.51 10.67 0.00 11.40 14.00 11.40 0.00 11.75 13.00
## [4189] 11.80 12.00 11.83 11.50 11.60 13.50 0.00 12.25 13.51 13.71 10.25 12.74
## [4201] 11.80 11.67 0.00 12.38 11.50 13.53 14.00 14.76 0.00 13.00 13.25 15.17
## [4213] 14.67 11.40 15.64 0.00 0.00 13.50 13.33 11.83 0.00 16.00 13.00 11.83
## [4225] 13.93 13.50 11.50 13.29 13.00 0.00 14.74 12.00 12.25 14.99 11.25 11.00
## [4237] 14.00 13.02 11.50 14.67 13.83 13.33 11.50 10.38 12.73 0.00 11.25 11.00
## [4249] 11.67 14.20 11.83 0.00 11.60 0.00 11.25 12.56 12.41 12.75 12.55 14.00
## [4261] 0.00 13.00 13.00 11.00 12.67 12.43 0.00 12.20 12.25 10.00 12.00 15.20
## [4273] 12.51 12.67 12.60 12.33 0.00 13.67 15.33 0.00 0.00 0.00 10.57 0.00
## [4285] 11.86 11.00 13.67 11.40 13.00 11.17 12.18 0.00 13.91 11.00 13.75 11.00
## [4297] 12.14 13.00 0.00 10.00 12.00 0.00 11.83 12.00 0.00 10.50 0.00 0.00
## [4309] 0.00 13.20 13.62 10.00 15.00 12.21 0.00 12.50 13.57 14.00 15.00 13.17
## [4321] 11.25 12.00 11.75 0.00 14.40 12.80 13.20 0.00 13.50 11.67 0.00 0.00
## [4333] 11.33 11.00 12.67 12.50 17.00 13.25 12.50 13.29 11.50 14.24 11.33 12.57
## [4345] 13.20 13.33 0.00 10.00 13.66 12.47 11.86 12.83 12.33 0.00 12.80 14.29
## [4357] 0.00 12.33 11.00 13.40 11.97 13.35 12.50 0.00 10.75 0.00 14.00 12.00
## [4369] 0.00 11.83 0.00 14.93 0.00 10.83 13.74 0.00 12.12 11.33 13.25 13.67
## [4381] 11.32 0.00 15.00 15.62 10.50 0.00 12.50 10.17 12.50 14.14 13.00 12.06
## [4393] 11.00 10.67 14.89 12.40 13.33 11.67 12.25 14.33 13.33 0.00 13.00 11.26
## [4405] 10.50 14.31 11.33 13.29 11.67 14.33 12.50 13.33 12.20 13.00 11.60 11.08
## [4417] 12.62 13.50 13.14 12.67 11.00 13.50 12.00 13.00round(podatki$grade_average,2)## [1] 0.00 13.83 0.00 12.91 12.67 11.68 13.82 0.00 14.01 12.45 13.27 13.21
## [13] 0.00 10.79 12.62 6.60 11.50 13.93 12.38 12.58 0.00 11.43 12.86 12.83
## [25] 13.71 11.30 12.33 12.83 12.17 13.32 11.21 13.12 12.42 13.52 12.91 5.00
## [37] 0.00 11.00 11.30 11.83 6.38 15.30 14.14 13.40 0.00 12.92 12.43 13.64
## [49] 12.39 12.58 13.92 11.83 12.50 15.26 10.80 13.32 0.00 12.95 14.94 0.00
## [61] 12.68 12.00 0.00 10.70 0.00 11.45 0.00 12.50 10.97 11.40 0.00 12.86
## [73] 0.00 11.83 12.33 10.60 10.75 13.50 14.95 11.83 12.20 0.00 12.73 11.67
## [85] 11.00 13.08 11.05 10.93 13.90 5.00 0.00 13.75 6.00 6.33 12.10 13.62
## [97] 13.50 14.11 14.00 5.98 13.14 0.00 0.00 14.43 0.00 12.64 0.00 13.72
## [109] 12.78 12.33 14.43 12.00 13.10 12.62 12.52 12.31 10.38 10.50 12.27 13.30
## [121] 11.00 11.03 0.00 13.50 13.18 6.05 13.97 13.10 13.33 14.24 13.49 12.67
## [133] 13.50 7.00 11.69 12.25 11.85 14.83 13.04 17.36 12.67 12.33 0.00 11.42
## [145] 12.97 11.40 0.00 11.43 13.77 14.02 0.00 12.90 11.58 12.57 11.33 11.75
## [157] 11.20 12.05 11.42 11.80 13.08 12.81 15.14 11.25 14.20 12.75 0.00 11.33
## [169] 14.26 11.67 10.88 13.01 11.68 11.83 12.46 12.58 12.60 11.95 11.40 14.47
## [181] 12.70 12.92 6.00 6.08 0.00 10.29 10.75 13.05 5.50 11.75 12.25 10.00
## [193] 0.00 0.00 12.24 0.00 12.93 0.00 13.50 11.58 14.04 11.25 12.32 11.94
## [205] 11.20 10.88 12.91 14.00 13.63 13.26 12.64 12.92 15.74 0.00 11.86 12.72
## [217] 11.60 5.00 5.00 6.75 12.67 13.92 11.88 13.02 14.33 15.57 12.40 12.43
## [229] 0.00 11.57 12.76 0.00 13.10 11.50 13.50 12.80 13.28 11.45 13.88 11.04
## [241] 11.97 13.23 12.60 0.00 12.63 13.22 13.15 12.04 11.79 13.70 12.40 13.92
## [253] 13.70 5.50 11.60 8.00 12.95 12.17 12.17 12.42 10.88 0.00 11.96 14.00
## [265] 12.42 11.96 14.83 12.10 12.75 13.67 12.73 11.50 12.92 13.11 14.96 14.54
## [277] 10.83 12.38 13.79 13.91 11.70 14.17 13.90 13.32 12.33 13.00 12.42 11.75
## [289] 11.17 13.38 15.08 14.08 12.21 11.67 11.67 14.73 13.92 11.95 12.82 12.86
## [301] 12.98 12.10 15.64 11.38 0.00 11.00 13.24 5.50 14.20 11.30 14.99 11.33
## [313] 11.50 13.53 5.25 16.30 14.71 14.02 11.57 12.42 0.00 13.06 14.18 11.90
## [325] 11.67 11.12 13.33 11.43 12.00 12.80 12.33 0.00 12.50 12.17 12.92 14.00
## [337] 14.79 13.39 12.30 11.88 12.00 0.00 12.85 13.55 12.50 13.00 11.50 11.33
## [349] 13.42 11.62 12.05 13.50 0.00 14.20 5.50 15.71 13.01 0.00 0.00 0.00
## [361] 11.75 11.33 10.67 13.61 13.98 15.95 14.03 11.10 13.76 13.41 13.56 11.04
## [373] 14.13 12.43 0.00 12.35 0.00 15.21 12.81 13.08 11.86 13.50 10.33 13.30
## [385] 11.83 11.33 13.00 11.64 12.78 14.42 11.88 11.67 12.20 11.42 14.43 12.86
## [397] 11.86 12.57 12.76 5.33 11.40 10.33 11.62 12.38 14.73 0.00 13.93 15.30
## [409] 14.62 0.00 14.65 12.40 12.83 14.80 12.08 14.70 13.80 11.30 11.60 0.00
## [421] 13.00 14.47 0.00 13.25 13.94 13.92 13.54 11.00 0.00 13.05 12.08 12.32
## [433] 12.90 0.00 14.39 13.81 10.88 14.08 0.00 11.30 8.00 12.00 12.30 12.69
## [445] 11.00 13.58 15.23 13.50 13.07 12.80 14.40 13.38 14.06 12.16 11.53 11.08
## [457] 0.00 12.80 13.97 12.92 15.50 13.64 10.55 11.20 10.50 11.12 13.48 13.13
## [469] 13.31 11.39 13.49 12.08 12.35 13.97 0.00 12.15 6.25 0.00 12.60 12.50
## [481] 12.83 14.31 0.00 12.83 12.45 12.43 11.04 11.57 14.59 12.68 12.44 14.10
## [493] 12.60 12.37 11.75 11.25 5.00 12.00 12.23 12.77 11.97 13.63 11.52 6.00
## [505] 11.72 13.26 14.28 13.17 13.50 0.00 5.38 0.00 12.12 0.00 0.00 0.00
## [517] 12.45 12.23 10.50 10.72 12.61 12.30 13.25 12.50 6.00 11.50 11.25 0.00
## [529] 0.00 12.69 11.67 0.00 11.69 0.00 0.00 11.39 7.00 11.70 13.01 11.92
## [541] 14.77 11.00 12.81 15.57 12.90 10.60 13.85 13.56 13.50 12.12 12.00 13.38
## [553] 12.72 5.50 0.00 11.64 11.50 0.00 11.08 12.51 12.05 11.83 10.67 13.35
## [565] 13.90 14.36 0.00 11.50 14.40 12.25 12.08 6.00 10.65 11.62 0.00 0.00
## [577] 13.83 10.40 11.58 13.56 0.00 12.58 14.06 12.40 11.70 15.10 12.60 12.56
## [589] 11.83 12.99 14.19 12.07 12.85 13.20 13.67 11.50 11.00 12.63 13.22 11.68
## [601] 0.00 12.30 16.32 12.42 14.43 0.00 0.00 12.36 0.00 11.98 13.21 13.58
## [613] 12.00 12.10 12.36 13.86 11.50 13.32 12.68 12.21 13.17 10.38 11.75 13.73
## [625] 13.00 11.40 11.11 13.42 13.58 11.90 12.04 12.60 14.17 11.35 13.75 12.42
## [637] 12.63 11.03 11.40 12.25 6.75 11.33 11.42 14.27 0.00 11.92 10.60 13.42
## [649] 12.72 11.12 15.90 13.58 12.61 11.85 11.38 10.70 10.30 11.19 12.40 0.00
## [661] 15.67 11.75 13.12 12.62 13.90 15.70 11.97 13.18 0.00 13.47 12.62 14.08
## [673] 12.01 12.43 12.83 10.50 14.50 11.92 7.50 0.00 10.75 13.57 14.20 0.00
## [685] 11.61 12.50 11.67 12.16 12.90 0.00 0.00 12.53 12.79 5.62 14.75 13.42
## [697] 13.67 10.40 12.16 17.17 12.60 13.83 13.19 0.00 13.98 13.17 12.32 14.17
## [709] 15.25 0.00 0.00 0.00 12.55 13.11 13.95 11.92 0.00 7.17 16.70 13.10
## [721] 12.33 12.50 0.00 5.50 0.00 15.89 14.40 0.00 0.00 12.47 12.08 11.90
## [733] 11.80 12.21 0.00 11.94 11.81 10.67 11.59 13.42 0.00 13.46 13.30 10.92
## [745] 14.00 0.00 11.17 11.96 0.00 13.71 12.54 14.00 13.11 0.00 13.83 0.00
## [757] 11.79 11.18 12.67 11.59 12.30 0.00 12.00 10.50 13.56 10.70 12.20 12.45
## [769] 14.10 14.58 15.14 0.00 13.35 12.25 12.00 12.00 15.31 13.29 13.08 13.17
## [781] 15.25 11.08 14.65 13.35 12.57 11.49 13.83 14.54 14.20 0.00 13.50 5.75
## [793] 11.88 12.80 12.67 14.50 13.11 13.02 13.50 12.46 11.50 0.00 12.90 14.75
## [805] 14.07 10.75 12.58 13.50 0.00 11.33 0.00 12.90 13.89 14.30 15.36 12.73
## [817] 12.00 13.67 13.31 12.83 11.80 0.00 13.96 12.93 12.00 14.00 12.37 15.58
## [829] 14.25 0.00 11.33 0.00 12.85 11.00 0.00 11.50 12.04 12.96 0.00 13.10
## [841] 0.00 12.75 0.00 14.02 11.10 0.00 11.20 10.46 13.48 14.01 13.29 11.93
## [853] 14.01 13.84 0.00 5.90 13.25 0.00 0.00 10.38 12.93 0.00 12.07 14.25
## [865] 13.75 14.87 0.00 0.00 13.33 0.00 12.82 15.50 11.52 11.39 14.75 13.24
## [877] 11.25 5.00 11.97 12.17 13.43 0.00 5.50 12.21 12.60 12.27 13.08 11.00
## [889] 14.68 12.12 14.33 0.00 14.43 0.00 12.15 12.17 12.75 12.94 10.92 13.50
## [901] 12.00 11.31 12.89 12.95 5.00 12.82 0.00 11.36 10.62 0.00 13.25 13.07
## [913] 10.80 11.60 0.00 13.33 0.00 0.00 14.58 12.58 11.07 11.17 12.00 11.00
## [925] 10.67 13.70 7.00 11.77 0.00 0.00 11.75 13.14 14.36 11.25 11.71 13.79
## [937] 10.38 12.71 12.46 11.20 12.70 13.14 0.00 0.00 15.68 12.92 13.22 0.00
## [949] 11.45 0.00 11.30 0.00 13.12 0.00 11.62 12.17 11.83 12.75 12.93 0.00
## [961] 11.58 13.55 13.43 12.08 10.93 12.90 0.00 0.00 0.00 10.58 14.25 5.00
## [973] 0.00 15.75 11.71 11.17 12.67 12.53 12.63 12.07 10.88 11.20 12.25 11.29
## [985] 13.00 13.71 15.34 5.40 11.00 13.00 15.53 13.40 11.21 13.83 13.55 14.25
## [997] 14.01 12.15 13.03 12.75 0.00 0.00 0.00 11.10 16.96 12.83 15.23 13.00
## [1009] 14.43 13.79 13.16 12.01 13.30 0.00 11.70 12.33 5.50 13.05 5.50 12.06
## [1021] 12.98 11.27 11.68 14.00 13.00 11.00 13.00 11.93 14.03 13.31 10.55 11.38
## [1033] 13.79 14.41 6.50 14.17 0.00 13.58 12.42 11.47 11.10 12.79 11.41 12.21
## [1045] 11.90 0.00 13.17 14.10 12.67 15.55 0.00 14.57 15.02 13.00 15.32 14.19
## [1057] 12.37 14.57 11.22 12.69 13.41 0.00 11.08 14.45 12.68 14.31 13.42 11.87
## [1069] 13.96 13.00 14.75 13.74 12.50 14.30 12.70 12.67 11.86 13.25 0.00 13.57
## [1081] 12.92 12.10 12.40 14.14 12.67 0.00 13.67 12.08 12.37 0.00 12.00 0.00
## [1093] 11.33 11.79 12.93 12.17 0.00 11.72 12.75 14.07 13.72 0.00 11.12 10.87
## [1105] 12.30 0.00 14.90 12.55 10.80 12.53 12.33 12.73 12.56 11.00 13.91 13.12
## [1117] 0.00 13.14 11.78 12.33 16.08 13.27 13.92 13.00 13.17 13.10 16.79 10.80
## [1129] 13.80 12.11 13.06 13.29 10.83 14.62 0.00 11.12 13.81 11.92 13.30 14.09
## [1141] 13.10 11.70 14.38 12.95 12.31 12.80 0.00 11.45 12.08 13.49 11.64 0.00
## [1153] 12.38 13.35 13.26 12.12 10.83 13.04 11.82 13.74 11.40 13.13 14.65 11.33
## [1165] 6.85 14.24 11.45 12.67 13.93 11.62 12.20 15.07 11.00 12.33 12.80 11.12
## [1177] 12.87 14.40 10.92 12.57 11.92 11.88 12.25 13.47 12.77 11.71 12.83 10.50
## [1189] 11.58 13.57 0.00 12.04 0.00 14.18 15.38 12.11 5.00 11.29 14.83 15.97
## [1201] 15.14 12.98 12.73 11.68 6.50 12.81 12.33 12.89 5.50 11.38 0.00 11.12
## [1213] 13.63 12.25 12.88 16.64 12.00 12.89 12.76 12.96 0.00 15.14 0.00 13.17
## [1225] 13.58 15.49 11.13 11.60 13.76 12.72 11.46 11.92 14.36 12.75 13.93 11.50
## [1237] 13.59 8.00 13.16 0.00 11.20 11.33 10.50 13.33 10.88 11.50 13.17 0.00
## [1249] 11.50 12.40 15.42 12.35 12.17 12.04 7.38 5.00 12.43 12.74 13.60 15.94
## [1261] 11.65 7.00 0.00 16.17 11.79 13.42 13.33 12.46 12.49 5.00 12.51 12.50
## [1273] 11.00 0.00 11.97 12.83 13.13 12.15 11.88 12.17 13.25 13.02 0.00 17.95
## [1285] 11.25 13.08 12.59 12.33 12.05 14.05 13.56 14.29 10.88 16.20 0.00 5.00
## [1297] 0.00 12.49 12.11 11.00 6.17 0.00 0.00 12.72 14.86 12.75 13.84 12.80
## [1309] 13.31 11.99 12.22 15.17 13.25 13.03 12.17 14.51 11.88 11.33 11.50 11.90
## [1321] 12.25 13.75 13.76 12.60 11.33 14.33 12.58 5.00 14.66 12.62 13.38 13.85
## [1333] 6.00 11.60 13.31 11.70 12.14 12.40 11.25 11.40 11.83 12.50 13.50 13.25
## [1345] 11.42 13.67 12.92 12.77 13.25 12.67 0.00 15.66 11.75 0.00 10.88 13.05
## [1357] 5.88 0.00 0.00 0.00 6.50 13.33 0.00 0.00 13.70 0.00 13.66 12.20
## [1369] 10.50 12.93 13.00 15.03 11.86 12.20 12.50 0.00 12.25 0.00 7.00 0.00
## [1381] 12.48 0.00 11.25 13.35 15.50 5.25 0.00 12.54 0.00 11.05 13.88 11.97
## [1393] 0.00 13.26 12.05 11.37 13.17 13.67 12.03 14.29 0.00 12.34 14.10 14.11
## [1405] 0.00 0.00 12.34 11.50 10.75 11.10 0.00 11.62 11.10 11.33 13.98 12.47
## [1417] 0.00 13.63 11.70 12.70 11.60 12.13 11.58 11.08 13.45 0.00 12.42 13.45
## [1429] 11.22 12.92 12.91 11.00 10.92 15.58 12.85 13.50 12.25 12.33 13.67 12.16
## [1441] 13.38 11.83 14.33 0.00 13.82 0.00 0.00 12.29 12.58 12.56 12.08 12.15
## [1453] 0.00 11.58 11.93 0.00 12.50 13.01 11.25 0.00 11.50 12.58 11.83 11.50
## [1465] 11.12 12.60 5.50 13.72 14.83 13.00 11.70 11.55 11.81 0.00 12.25 12.30
## [1477] 12.00 13.33 7.25 6.60 13.48 11.29 14.80 12.28 10.98 11.12 13.84 11.74
## [1489] 0.00 13.92 14.81 11.25 10.62 12.30 0.00 13.97 14.14 13.43 12.17 13.02
## [1501] 13.93 6.00 14.02 12.09 12.46 11.50 10.50 0.00 13.50 0.00 0.00 11.25
## [1513] 0.00 13.92 0.00 14.14 0.00 13.58 0.00 0.00 5.00 15.20 6.40 11.08
## [1525] 0.00 12.83 12.55 11.20 12.38 11.33 13.00 13.03 11.96 15.35 14.00 12.38
## [1537] 0.00 12.33 11.83 0.00 11.23 0.00 5.00 0.00 12.12 12.25 12.20 0.00
## [1549] 0.00 0.00 12.34 10.53 10.69 13.67 14.50 13.53 0.00 0.00 0.00 13.25
## [1561] 12.80 13.93 13.20 11.50 13.58 12.90 15.23 11.07 5.83 0.00 13.93 0.00
## [1573] 0.00 12.38 12.39 0.00 12.57 12.12 12.50 0.00 13.83 11.00 5.50 11.60
## [1585] 13.00 0.00 12.12 10.98 11.25 12.42 5.50 0.00 10.92 0.00 11.12 11.75
## [1597] 12.67 15.86 11.90 11.29 0.00 13.27 10.67 12.87 5.75 12.09 13.00 12.89
## [1609] 13.13 12.70 11.58 12.70 12.13 0.00 11.67 11.83 14.12 11.60 13.08 12.32
## [1621] 14.31 12.33 10.75 12.13 10.97 5.00 14.25 11.75 12.38 0.00 12.00 0.00
## [1633] 13.90 13.06 12.00 12.81 12.50 12.50 0.00 14.55 12.52 14.51 14.09 11.50
## [1645] 11.20 0.00 13.71 14.01 12.52 14.36 14.51 14.70 14.60 14.03 6.75 12.47
## [1657] 13.20 11.12 0.00 0.00 14.44 16.12 15.44 14.26 12.96 14.50 11.83 13.76
## [1669] 10.80 12.88 11.75 14.65 12.64 14.42 12.77 5.20 0.00 11.55 13.82 5.96
## [1681] 12.33 12.46 11.80 11.88 13.58 14.83 6.14 6.33 0.00 0.00 0.00 0.00
## [1693] 13.86 12.10 0.00 13.31 11.78 0.00 8.07 0.00 15.63 14.08 0.00 12.00
## [1705] 12.64 12.50 0.00 11.50 13.04 12.45 12.12 13.38 11.75 12.00 12.46 13.34
## [1717] 13.60 10.00 7.25 0.00 12.07 10.99 14.79 11.78 12.33 11.67 12.97 11.38
## [1729] 0.00 12.55 12.20 12.50 11.58 11.67 11.21 13.28 13.05 12.89 14.00 0.00
## [1741] 13.13 12.10 13.52 10.83 7.00 11.25 11.67 0.00 0.00 11.97 11.77 0.00
## [1753] 11.90 5.25 0.00 14.20 12.49 6.33 14.71 12.86 12.25 0.00 15.89 10.88
## [1765] 12.62 0.00 14.17 14.40 0.00 11.17 13.12 10.25 13.96 11.83 10.40 0.00
## [1777] 12.11 11.40 11.20 14.11 12.53 12.33 15.57 11.50 15.01 11.25 0.00 13.62
## [1789] 5.62 11.74 13.08 0.00 12.25 0.00 12.73 13.51 12.50 13.33 13.07 6.17
## [1801] 12.29 12.81 12.15 11.49 0.00 0.00 11.65 0.00 12.10 12.67 12.63 13.16
## [1813] 12.35 11.75 0.00 14.31 11.68 13.00 0.00 14.32 12.33 11.88 5.50 11.08
## [1825] 13.58 14.44 13.81 10.92 0.00 11.79 12.25 12.75 11.70 11.48 14.38 11.45
## [1837] 12.24 12.16 13.43 15.33 0.00 5.25 11.40 12.30 12.72 12.30 12.96 10.38
## [1849] 13.09 11.75 0.00 14.04 12.20 14.33 11.00 0.00 12.35 11.95 13.25 12.50
## [1861] 0.00 5.50 5.25 12.50 0.00 12.40 5.25 0.00 14.46 12.17 0.00 6.50
## [1873] 15.34 0.00 12.46 13.30 0.00 0.00 0.00 13.56 14.48 11.17 0.00 0.00
## [1885] 11.74 12.18 11.42 0.00 14.67 0.00 0.00 13.44 6.75 0.00 11.84 10.75
## [1897] 11.75 11.85 0.00 14.25 13.00 12.28 14.56 13.12 12.25 13.75 14.77 12.94
## [1909] 11.67 14.27 13.50 12.48 14.37 5.33 13.80 13.45 12.60 12.71 11.80 13.40
## [1921] 13.85 13.92 11.40 12.85 7.00 13.94 12.61 12.96 12.40 14.99 13.12 13.45
## [1933] 11.12 13.37 12.82 13.90 12.90 13.68 12.50 12.00 12.87 13.17 14.75 12.03
## [1945] 13.50 14.83 14.04 12.50 13.33 12.05 0.00 0.00 0.00 12.14 12.46 12.67
## [1957] 11.67 14.81 11.16 13.06 12.75 0.00 13.40 13.22 10.79 13.64 12.67 11.97
## [1969] 11.96 14.53 11.81 13.49 12.16 11.80 13.19 12.20 12.74 13.00 13.64 14.00
## [1981] 11.88 11.58 13.14 13.97 14.14 11.68 14.66 0.00 12.83 11.72 12.50 0.00
## [1993] 11.54 12.00 0.00 11.50 13.48 13.10 5.00 10.80 10.81 6.92 12.73 11.83
## [2005] 0.00 13.80 14.50 13.17 0.00 0.00 12.50 12.10 11.90 0.00 0.00 12.39
## [2017] 12.40 13.88 12.30 13.75 0.00 0.00 0.00 11.89 11.62 12.37 0.00 0.00
## [2029] 12.97 13.75 14.25 6.08 12.46 0.00 13.23 14.44 10.00 11.75 11.55 12.08
## [2041] 11.33 12.51 13.58 12.33 12.90 12.81 0.00 12.36 14.29 13.44 10.92 11.81
## [2053] 5.00 13.25 13.14 13.83 12.74 12.50 12.03 12.50 13.52 13.39 13.33 12.50
## [2065] 12.90 14.50 13.05 12.75 11.83 11.17 12.31 12.92 13.54 14.20 13.83 14.57
## [2077] 12.00 14.38 12.77 14.15 12.47 14.15 14.06 14.76 13.73 0.00 0.00 15.08
## [2089] 12.63 11.90 14.23 11.77 15.70 15.20 15.97 12.71 0.00 12.20 13.78 11.92
## [2101] 11.82 11.40 13.77 11.33 13.15 12.78 13.75 13.27 11.65 13.71 14.17 14.67
## [2113] 15.98 11.26 11.12 0.00 12.14 12.83 13.53 0.00 6.50 11.64 12.20 5.64
## [2125] 0.00 5.00 13.76 12.76 0.00 12.96 12.38 12.12 11.77 13.28 13.61 0.00
## [2137] 11.83 12.42 13.20 12.25 12.56 12.39 12.73 0.00 12.67 13.28 13.12 12.25
## [2149] 14.50 13.28 13.57 12.04 13.70 13.14 14.90 15.10 0.00 14.07 13.77 10.67
## [2161] 14.57 11.38 0.00 13.79 15.08 13.33 14.96 11.60 12.60 16.37 13.71 12.65
## [2173] 13.00 6.50 12.38 0.00 14.67 11.25 14.21 12.69 0.00 10.65 13.66 12.53
## [2185] 11.00 12.29 11.57 13.40 12.00 12.27 0.00 0.00 16.08 11.00 0.00 12.14
## [2197] 11.38 11.00 10.50 0.00 6.25 11.95 11.85 0.00 12.50 14.13 0.00 6.67
## [2209] 11.45 0.00 13.10 13.33 11.10 12.29 15.23 11.80 13.52 11.30 14.08 14.67
## [2221] 12.74 12.55 11.96 0.00 14.94 10.25 13.17 0.00 13.90 11.29 0.00 0.00
## [2233] 5.00 11.58 11.33 0.00 12.88 0.00 11.33 0.00 12.60 11.04 11.25 13.68
## [2245] 10.00 13.00 12.47 0.00 0.00 13.43 13.17 11.85 13.95 0.00 5.50 14.02
## [2257] 12.31 11.08 12.33 13.01 12.92 5.75 6.75 15.05 12.10 14.40 13.25 0.00
## [2269] 11.66 0.00 0.00 13.07 11.24 0.00 0.00 11.08 13.30 13.04 11.20 6.07
## [2281] 12.68 11.12 10.92 12.10 12.46 0.00 12.20 14.03 11.65 0.00 14.25 10.90
## [2293] 12.50 13.08 0.00 14.28 5.00 11.20 11.62 0.00 14.00 11.57 10.83 13.27
## [2305] 0.00 11.92 6.50 0.00 0.00 13.60 13.93 12.94 6.38 14.55 12.17 15.50
## [2317] 14.67 0.00 0.00 14.21 6.12 16.25 12.00 14.09 10.33 5.00 5.00 10.58
## [2329] 0.00 0.00 0.00 0.00 12.87 0.00 13.95 12.00 10.72 0.00 13.92 14.76
## [2341] 0.00 13.58 11.58 13.00 11.81 13.99 12.88 13.73 0.00 12.08 13.61 13.58
## [2353] 14.10 13.28 0.00 13.96 0.00 11.84 14.86 11.00 10.50 0.00 11.57 5.83
## [2365] 12.25 14.17 12.03 13.83 15.15 15.67 11.53 0.00 0.00 13.00 12.88 12.12
## [2377] 14.50 0.00 11.29 13.00 12.76 13.75 14.15 11.62 5.75 12.92 12.03 0.00
## [2389] 11.65 0.00 11.71 12.05 12.92 0.00 12.12 11.83 0.00 11.90 14.50 12.10
## [2401] 11.25 12.00 11.50 15.89 12.26 14.08 0.00 0.00 0.00 11.12 0.00 5.62
## [2413] 11.58 11.23 11.40 0.00 10.75 11.08 12.61 13.49 0.00 0.00 13.49 0.00
## [2425] 0.00 0.00 0.00 11.50 11.26 12.14 12.05 16.00 12.58 12.50 5.83 12.80
## [2437] 12.90 12.42 12.71 7.00 0.00 11.20 5.00 18.28 0.00 11.97 14.85 12.50
## [2449] 0.00 13.51 0.00 6.00 12.30 14.08 0.00 14.90 14.00 11.50 0.00 12.40
## [2461] 5.88 0.00 0.00 0.00 11.53 5.79 13.00 13.07 12.71 0.00 11.30 0.00
## [2473] 10.79 0.00 14.67 0.00 13.50 12.43 11.90 11.00 0.00 12.53 14.02 12.44
## [2485] 14.82 11.75 0.00 0.00 12.58 13.61 11.96 12.15 10.46 13.75 13.33 13.42
## [2497] 0.00 12.75 0.00 12.50 13.35 12.83 12.41 12.79 0.00 13.59 11.29 11.93
## [2509] 0.00 13.81 6.00 12.00 13.13 12.75 13.07 12.12 12.08 12.21 12.83 12.89
## [2521] 13.00 11.65 13.48 0.00 5.83 12.08 13.67 14.05 14.73 12.11 12.00 12.91
## [2533] 11.83 12.92 12.50 11.07 15.00 15.27 13.25 11.95 7.00 6.42 14.09 0.00
## [2545] 11.58 15.17 12.83 13.23 14.08 5.00 12.80 13.42 12.00 5.25 11.00 10.50
## [2557] 11.70 0.00 11.08 13.75 13.05 13.07 5.38 6.00 13.67 12.88 14.13 10.93
## [2569] 11.90 14.17 14.40 15.93 13.40 14.98 14.00 15.02 11.25 10.25 13.98 12.92
## [2581] 13.33 0.00 14.90 11.62 13.92 12.10 12.33 10.75 11.42 12.20 0.00 12.33
## [2593] 11.25 11.92 11.00 12.42 11.80 0.00 12.50 12.70 13.15 11.79 12.56 0.00
## [2605] 11.75 13.00 13.20 13.07 11.88 10.50 13.07 13.50 16.00 0.00 12.70 12.30
## [2617] 6.10 11.90 12.37 13.70 11.73 11.92 12.66 10.75 12.17 6.00 14.62 12.20
## [2629] 11.28 13.54 11.50 5.38 12.55 12.67 12.86 5.88 5.50 0.00 12.80 12.35
## [2641] 0.00 11.75 6.17 12.50 13.32 0.00 12.71 11.90 12.42 12.00 13.60 13.10
## [2653] 13.65 0.00 13.87 12.68 0.00 12.25 0.00 11.60 11.04 14.18 12.09 0.00
## [2665] 14.08 11.12 13.48 11.00 11.64 6.12 11.89 13.73 11.50 11.75 12.65 10.96
## [2677] 6.58 14.62 0.00 16.30 12.53 6.39 5.00 11.83 0.00 11.40 10.50 0.00
## [2689] 0.00 6.00 10.88 12.55 11.70 15.58 12.08 13.95 0.00 12.82 12.68 13.40
## [2701] 0.00 5.00 0.00 11.22 0.00 12.33 12.57 0.00 13.40 12.00 14.83 0.00
## [2713] 5.75 12.40 16.55 13.27 0.00 14.33 14.12 13.98 13.77 11.38 12.71 11.00
## [2725] 12.41 10.75 13.93 14.31 14.96 12.70 13.77 12.15 14.01 11.83 13.40 15.40
## [2737] 14.66 10.93 11.67 14.05 13.27 12.42 13.92 14.12 10.92 13.29 12.10 0.00
## [2749] 0.00 11.55 0.00 13.82 0.00 13.30 13.60 11.81 10.00 0.00 0.00 11.40
## [2761] 13.18 10.92 12.00 12.54 11.12 13.11 14.41 0.00 12.27 5.00 13.71 13.04
## [2773] 12.86 14.25 12.65 15.08 0.00 13.18 13.18 12.07 13.45 10.67 11.17 12.93
## [2785] 12.97 13.09 12.50 11.17 0.00 0.00 11.75 14.50 11.79 0.00 0.00 12.76
## [2797] 0.00 13.67 13.07 11.50 15.75 0.00 14.94 16.02 11.26 12.04 11.80 14.38
## [2809] 12.42 12.75 12.67 12.56 13.71 11.12 0.00 11.66 14.27 12.43 12.55 5.50
## [2821] 12.77 0.00 14.54 13.94 12.71 12.54 13.37 11.17 12.58 0.00 12.10 11.80
## [2833] 13.58 11.50 14.23 12.55 0.00 12.77 0.00 16.25 11.50 11.80 12.93 0.00
## [2845] 10.75 13.14 7.00 0.00 11.78 13.70 0.00 14.25 11.32 14.04 0.00 12.85
## [2857] 14.17 0.00 13.10 12.75 12.50 12.10 12.25 12.22 11.50 16.50 0.00 13.75
## [2869] 13.75 14.60 10.93 0.00 11.00 12.54 0.00 11.73 0.00 11.92 12.44 12.08
## [2881] 11.72 11.10 11.00 11.92 14.77 13.98 12.10 12.99 12.80 13.90 13.12 0.00
## [2893] 12.80 12.22 12.83 10.92 11.62 14.09 12.41 0.00 11.47 0.00 12.06 13.75
## [2905] 12.00 12.50 11.33 14.07 13.56 11.93 0.00 13.28 0.00 14.56 0.00 11.23
## [2917] 13.96 12.65 11.38 0.00 0.00 6.62 11.87 5.50 12.76 14.58 14.20 10.82
## [2929] 0.00 13.67 6.25 6.50 0.00 11.97 0.00 14.12 0.00 6.38 10.88 0.00
## [2941] 12.27 12.36 14.04 13.42 12.23 11.62 0.00 12.76 12.33 11.25 13.36 14.25
## [2953] 11.87 0.00 14.40 0.00 0.00 11.82 11.67 13.92 12.21 14.14 11.50 11.15
## [2965] 12.89 13.10 13.87 0.00 12.33 12.90 12.55 11.83 12.50 11.97 0.00 14.62
## [2977] 12.58 13.33 13.25 13.68 12.33 13.56 14.19 14.05 14.35 13.92 11.88 12.58
## [2989] 13.12 11.47 13.75 11.82 0.00 12.53 12.21 14.38 12.82 11.25 14.17 0.00
## [3001] 12.71 12.81 13.10 12.76 12.90 14.76 11.12 10.88 14.50 13.72 14.38 13.14
## [3013] 13.66 13.67 0.00 14.67 14.16 14.11 12.98 11.07 12.42 14.34 12.62 0.00
## [3025] 0.00 14.00 12.57 11.67 13.81 11.25 12.17 14.64 12.43 13.67 12.33 11.08
## [3037] 0.00 13.58 13.33 11.92 13.07 13.07 12.97 12.10 12.58 11.88 11.29 13.68
## [3049] 13.47 13.07 11.30 11.18 15.93 12.80 14.29 13.83 13.83 0.00 12.63 14.23
## [3061] 14.50 5.00 11.62 13.25 11.85 0.00 12.38 12.11 12.43 0.00 10.95 0.00
## [3073] 11.80 12.83 11.99 12.20 12.50 0.00 11.53 13.00 14.68 12.94 12.59 0.00
## [3085] 11.85 12.42 11.81 12.17 15.94 0.00 10.48 13.02 13.33 14.57 5.00 11.86
## [3097] 13.17 5.62 11.63 6.00 13.40 12.60 11.62 0.00 12.21 15.37 12.32 14.28
## [3109] 12.83 15.87 0.00 15.06 12.00 12.49 11.58 14.17 0.00 13.45 11.15 12.33
## [3121] 12.12 11.10 11.12 14.65 14.29 12.17 11.02 13.20 13.40 12.75 11.88 12.79
## [3133] 13.89 13.54 12.85 0.00 12.25 16.68 14.08 11.85 15.39 11.68 5.50 15.11
## [3145] 14.89 11.57 11.33 11.91 10.96 10.68 12.75 0.00 14.75 15.17 11.98 10.67
## [3157] 11.62 10.17 12.92 11.17 0.00 12.33 14.33 15.67 13.00 13.05 12.25 10.58
## [3169] 12.38 11.29 12.40 11.97 12.22 12.37 11.08 0.00 13.21 13.00 14.54 11.20
## [3181] 14.83 12.90 11.42 10.75 13.75 0.00 0.00 0.00 5.00 0.00 0.00 12.80
## [3193] 11.12 11.81 11.63 0.00 12.07 12.63 0.00 12.84 0.00 13.50 12.08 10.90
## [3205] 6.50 0.00 13.17 11.57 11.25 10.88 16.34 0.00 12.37 0.00 14.83 12.92
## [3217] 10.60 11.46 11.29 0.00 5.00 12.18 14.98 0.00 12.62 13.81 13.08 11.85
## [3229] 12.50 13.40 14.99 11.38 12.55 0.00 13.72 14.04 13.20 12.33 14.18 12.83
## [3241] 10.53 12.17 11.12 14.11 11.53 12.00 14.17 14.46 11.50 14.08 4.90 10.86
## [3253] 0.00 12.67 12.62 11.32 12.77 12.63 13.20 14.32 12.38 13.00 0.00 14.78
## [3265] 11.70 11.92 13.70 11.73 0.00 12.44 11.00 12.48 12.82 12.00 6.00 11.03
## [3277] 11.50 14.06 11.50 10.92 13.68 13.10 11.91 11.08 11.50 13.80 6.00 10.71
## [3289] 11.25 11.59 7.00 6.50 11.00 13.68 12.36 10.88 12.37 12.21 14.12 0.00
## [3301] 0.00 14.13 13.39 14.10 14.25 13.33 13.51 12.94 13.42 0.00 12.17 15.31
## [3313] 10.58 12.63 0.00 14.50 13.50 0.00 10.00 11.60 12.42 0.00 5.25 13.04
## [3325] 0.00 10.50 12.17 5.00 14.00 11.21 11.36 12.08 11.25 10.83 12.53 5.00
## [3337] 6.25 12.20 11.67 10.84 0.00 12.70 12.75 11.50 11.83 12.50 0.00 0.00
## [3349] 11.49 6.00 11.75 11.25 11.50 12.27 15.30 5.75 12.80 0.00 0.00 11.50
## [3361] 12.90 13.75 11.70 0.00 11.15 12.25 11.75 14.62 14.06 11.17 0.00 12.19
## [3373] 12.58 12.35 12.33 13.14 14.58 12.50 11.48 13.90 12.92 12.08 14.65 0.00
## [3385] 12.92 10.76 14.48 12.54 13.00 11.45 12.50 12.89 12.83 11.70 13.65 13.84
## [3397] 6.62 14.50 14.35 11.92 13.19 13.59 13.33 13.80 10.72 0.00 12.00 14.15
## [3409] 0.00 13.33 13.71 12.45 5.50 0.00 13.11 14.16 12.33 5.50 13.86 13.67
## [3421] 13.26 0.00 12.08 15.00 0.00 6.17 10.90 11.50 13.42 0.00 14.75 14.20
## [3433] 14.75 14.02 13.92 12.42 13.46 10.42 11.69 11.88 11.98 12.65 11.95 13.25
## [3445] 11.52 12.36 15.19 0.00 13.00 14.54 12.21 13.44 11.57 12.66 10.00 13.44
## [3457] 13.04 14.67 11.86 0.00 12.90 13.13 11.58 11.07 13.46 0.00 11.75 11.26
## [3469] 10.82 12.77 13.80 13.42 0.00 12.10 0.00 15.06 14.80 11.95 10.50 13.08
## [3481] 12.94 0.00 0.00 12.94 12.00 11.37 13.00 0.00 12.42 11.58 0.00 0.00
## [3493] 5.00 0.00 11.57 14.80 11.15 12.47 13.08 0.00 13.10 6.75 13.00 11.73
## [3505] 12.58 0.00 0.00 11.55 11.75 12.33 12.76 13.70 0.00 7.00 11.46 12.12
## [3517] 0.00 6.00 12.00 11.61 13.16 11.45 14.15 10.17 14.40 13.11 11.40 12.07
## [3529] 12.90 13.09 13.57 13.22 14.20 0.00 5.50 11.67 0.00 0.00 11.38 12.92
## [3541] 5.00 12.25 12.50 13.63 10.92 13.27 13.35 0.00 0.00 13.48 12.36 0.00
## [3553] 12.33 17.11 13.18 13.47 11.48 0.00 12.40 13.55 6.53 13.73 0.00 16.00
## [3565] 0.00 10.67 14.50 13.90 13.45 0.00 11.60 16.10 10.44 0.00 13.37 14.57
## [3577] 10.35 10.25 0.00 14.83 13.11 12.96 0.00 11.50 13.18 13.25 0.00 13.08
## [3589] 13.92 0.00 0.00 13.15 12.75 12.40 11.45 12.62 13.04 12.83 12.73 14.80
## [3601] 0.00 12.92 12.83 11.90 12.00 12.78 11.40 0.00 15.19 0.00 12.05 14.26
## [3613] 12.25 11.25 12.49 11.90 14.60 12.70 13.17 13.42 11.62 15.60 14.58 5.50
## [3625] 11.71 11.50 11.29 11.68 0.00 14.06 12.68 11.25 12.25 12.71 12.75 14.93
## [3637] 12.33 12.76 14.18 13.64 13.08 0.00 12.83 12.67 11.77 12.55 12.28 0.00
## [3649] 12.33 10.83 12.99 12.54 14.21 12.18 12.50 12.83 12.83 13.87 12.62 12.88
## [3661] 0.00 13.77 12.47 12.63 13.75 12.51 14.01 0.00 12.67 12.49 13.92 15.25
## [3673] 13.57 12.79 12.83 12.58 11.07 6.50 15.58 12.33 0.00 11.10 0.00 0.00
## [3685] 11.25 15.81 11.23 6.00 11.93 13.50 11.18 10.50 7.00 12.55 0.00 11.67
## [3697] 12.03 10.65 12.37 0.00 12.12 12.72 0.00 0.00 14.08 13.32 11.22 0.00
## [3709] 12.23 11.79 12.12 0.00 10.54 0.00 0.00 13.42 11.50 0.00 5.25 6.75
## [3721] 5.50 5.00 0.00 11.33 12.22 11.53 0.00 14.12 14.33 14.50 12.34 13.35
## [3733] 0.00 12.54 11.22 13.20 12.92 11.42 14.10 5.75 13.26 13.38 13.75 15.01
## [3745] 0.00 0.00 12.83 6.88 0.00 13.92 13.94 14.64 11.93 14.85 6.00 14.65
## [3757] 12.00 13.47 11.90 0.00 11.85 0.00 13.14 11.42 11.85 13.12 12.83 5.67
## [3769] 12.60 13.18 0.00 12.13 13.46 0.00 13.65 12.50 13.19 12.92 13.45 12.33
## [3781] 13.15 12.83 12.64 12.86 13.38 11.83 0.00 5.50 11.42 12.92 14.03 10.83
## [3793] 0.00 0.00 12.00 13.60 12.69 0.00 14.05 0.00 0.00 13.54 12.41 12.40
## [3805] 10.38 10.38 13.50 13.33 13.09 12.68 12.86 12.00 12.11 16.70 12.06 12.71
## [3817] 11.25 12.41 0.00 0.00 12.25 0.00 15.00 12.62 7.50 0.00 13.04 12.90
## [3829] 7.00 15.50 12.37 13.22 11.64 0.00 13.17 11.90 6.00 10.67 10.00 0.00
## [3841] 11.42 11.54 5.88 10.50 13.40 0.00 6.00 0.00 11.74 13.75 0.00 11.90
## [3853] 5.50 10.65 5.50 16.75 13.39 14.54 0.00 10.50 11.38 5.50 12.42 11.49
## [3865] 11.42 6.00 0.00 14.54 12.58 12.58 14.54 12.02 12.73 6.25 0.00 0.00
## [3877] 13.61 14.20 13.55 11.38 14.43 14.42 11.05 10.72 15.68 11.42 14.75 10.57
## [3889] 13.17 13.18 12.75 13.80 13.38 11.25 13.54 13.18 5.50 12.31 12.60 11.93
## [3901] 13.90 11.25 13.03 10.67 0.00 11.17 13.96 13.08 14.31 0.00 11.63 15.61
## [3913] 11.20 12.50 12.21 13.50 12.50 12.83 13.00 12.91 11.00 13.26 12.45 12.94
## [3925] 11.62 5.00 14.34 13.07 0.00 11.53 13.75 13.68 13.03 10.00 0.00 11.75
## [3937] 11.50 11.75 14.67 14.66 12.19 0.00 11.50 0.00 0.00 14.07 0.00 0.00
## [3949] 12.00 13.80 14.42 0.00 14.21 12.70 11.00 0.00 12.70 12.90 14.86 14.93
## [3961] 0.00 15.05 13.38 13.17 11.19 13.01 11.33 0.00 12.83 11.70 12.98 12.75
## [3973] 11.10 12.03 12.71 14.47 13.20 13.80 15.00 12.80 12.74 15.25 12.33 13.00
## [3985] 0.00 12.58 12.12 15.25 13.00 12.08 14.76 10.50 12.50 12.15 12.00 5.25
## [3997] 12.00 11.64 13.39 13.61 0.00 0.00 13.42 13.52 13.23 0.00 13.06 7.20
## [4009] 6.00 0.00 0.00 10.65 0.00 15.83 14.82 11.17 11.62 0.00 13.58 13.95
## [4021] 5.67 12.52 11.93 12.25 5.83 11.20 12.27 13.07 13.85 6.92 12.50 13.08
## [4033] 13.75 0.00 0.00 0.00 13.92 10.70 15.48 11.86 14.05 12.94 12.30 12.29
## [4045] 12.83 0.00 12.93 13.90 13.82 13.09 0.00 12.17 11.29 12.57 14.62 12.00
## [4057] 13.33 13.12 14.08 0.00 14.92 12.77 15.62 12.52 11.54 13.08 11.92 0.00
## [4069] 12.20 11.42 14.33 10.88 13.08 13.75 12.84 0.00 13.97 5.50 14.07 13.19
## [4081] 0.00 11.25 11.62 13.43 0.00 13.33 13.00 13.29 10.41 12.50 11.28 12.93
## [4093] 6.93 12.15 14.12 15.43 14.67 11.60 0.00 0.00 12.48 11.67 13.55 11.47
## [4105] 13.94 12.12 12.53 13.78 15.11 11.10 15.80 14.69 12.16 0.00 14.92 12.58
## [4117] 13.67 14.20 12.70 13.33 12.49 16.64 10.48 14.72 12.45 11.97 12.75 12.00
## [4129] 14.59 12.67 14.41 12.08 12.22 11.90 11.25 11.90 11.86 12.64 12.92 11.32
## [4141] 0.00 16.00 11.33 12.28 11.29 0.00 12.28 11.38 10.50 13.42 15.01 13.17
## [4153] 14.07 0.00 11.17 14.21 13.24 12.75 12.56 13.58 12.07 12.20 11.58 11.58
## [4165] 0.00 13.38 12.03 13.92 11.12 0.00 12.04 5.50 14.00 14.55 13.25 12.07
## [4177] 12.58 12.06 13.23 14.33 12.08 0.00 11.80 14.40 11.20 0.00 12.88 12.42
## [4189] 11.78 12.17 11.75 12.08 11.93 12.39 5.75 11.96 13.51 13.36 12.62 12.74
## [4201] 11.78 11.92 0.00 12.89 11.65 13.53 14.08 14.70 0.00 13.30 13.04 14.92
## [4213] 14.00 12.40 14.47 0.00 0.00 12.92 13.42 12.42 6.25 16.50 13.25 12.27
## [4225] 13.46 13.04 11.50 13.39 13.30 6.00 14.84 11.62 11.46 14.99 10.88 11.12
## [4237] 13.17 13.02 11.42 15.40 14.33 13.33 11.25 11.04 12.53 0.00 11.58 11.42
## [4249] 12.00 14.25 11.83 5.00 11.80 6.10 11.29 13.20 12.41 12.71 12.55 13.50
## [4261] 0.00 12.61 13.14 11.33 13.11 12.80 0.00 11.93 11.62 11.50 12.83 14.90
## [4273] 12.51 13.33 12.88 12.67 6.50 11.83 14.83 0.00 5.50 5.62 10.66 5.50
## [4285] 11.36 11.38 13.23 11.87 12.17 11.38 11.55 0.00 13.77 10.67 13.74 11.31
## [4297] 11.82 13.50 5.67 10.00 11.86 0.00 11.30 11.80 6.88 10.75 0.00 0.00
## [4309] 0.00 12.77 13.53 5.00 14.88 12.34 0.00 12.08 12.79 13.00 15.12 12.78
## [4321] 11.79 11.75 11.97 5.25 14.40 12.82 12.60 0.00 13.58 11.76 0.00 0.00
## [4333] 12.27 11.86 12.58 11.58 17.00 13.12 12.58 13.29 11.58 14.24 12.17 13.32
## [4345] 12.52 13.08 5.00 10.50 13.88 12.47 11.85 12.67 12.00 0.00 11.57 15.23
## [4357] 6.33 11.42 11.25 13.20 11.97 13.35 12.25 5.25 11.12 0.00 13.79 13.35
## [4369] 0.00 11.83 0.00 14.05 0.00 11.92 13.74 0.00 12.17 11.20 13.34 12.53
## [4381] 11.32 0.00 15.00 14.40 10.75 0.00 12.42 11.21 12.21 14.24 12.50 12.91
## [4393] 11.12 11.50 14.89 12.28 13.00 12.13 12.62 14.10 12.04 7.33 12.80 11.84
## [4405] 10.75 14.31 11.67 13.06 11.53 14.47 13.00 12.92 12.60 12.30 11.70 11.71
## [4417] 12.62 13.67 12.82 13.13 11.50 14.21 12.90 12.33head(podatki[,-c(13,14,15)])## Marital.status evening.attendance Educational.special.needs Gender
## 1 1 1 0 1
## 2 1 1 0 1
## 3 1 1 0 1
## 4 1 1 0 0
## 5 2 0 0 0
## 6 2 0 0 1
## Scholarship.holder Age.at.enrollment Curricular.units.1st.sem..grade.
## 1 0 20 0.00000
## 2 0 19 14.00000
## 3 0 19 0.00000
## 4 0 20 13.42857
## 5 0 45 12.33333
## 6 0 50 11.85714
## Curricular.units.2nd.sem..grade. grade_average
## 1 0.00000 0.00000
## 2 13.66667 13.83333
## 3 0.00000 0.00000
## 4 12.40000 12.91429
## 5 13.00000 12.66667
## 6 11.50000 11.67857Zanima nas,ali se povprečna ocena anketirancev razlikuje glede na to, ali oseba študij obiskuje podnevi ali zvečer.Izvedli bomo preizkus domneve o razliki med dvema aritmetičnima sredinama v neodvisnih vzorcih oz. preizkus skupin. H0: Povprečna ocena se med dnevnimi in nočnimi študenti ne razlikuje. H1: Povprečna ocena se med dnevnimi in nočnimi študenti razlikuje. Najprej si pogledamo opisne statistike.
## evening daytime
## 483 3941summary(podatki$grade_average)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 11.00 12.25 10.44 13.27 18.28Opazimo, da je oseb, ki študij obiskujejo podnevi občutno več kot tistih, ki ga obiskujejo zvečer. Povprečna ocena vseh je 10,44, vrednosti pa se gibljejo med 0 in 18,28.
Preveriti moramo še predpostavko o normalnosti porazdelitve spremenljivke grade_average na obeh skupinah.
library(rstatix)##
## Attaching package: 'rstatix'## The following object is masked from 'package:stats':
##
## filterpodatki %>%
group_by(evening.attendanceF) %>%
shapiro_test(grade_average)## # A tibble: 2 × 4
## evening.attendanceF variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 evening grade_average 0.742 9.86e-27
## 2 daytime grade_average 0.715 2.46e-63Podatki so izrazito nenormalno porazdeljeni na obeh skupinah ljudi. Potrebni bodo neparametrični testi.
library(psych)
describeBy(podatki$grade_average, podatki$evening.attendanceF)##
## Descriptive statistics by group
## group: evening
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 483 9.62 4.97 11.62 10.19 1.61 0 16.7 16.7 -1.17 -0.2 0.23
## ------------------------------------------------------------
## group: daytime
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3941 10.54 4.79 12.33 11.3 1.64 0 18.28 18.28 -1.47 0.66 0.08Aritmetična sredita je večja pri skupini, ki so šolo obiskovali podnevi, kot tista, ki šolo obiskuje zvečer. Zanima nas,ali je razlika med skupinama statistično značilna. Najvišja ocena, ki je dosežena v skupini ljudi, ki šolo obiskujejo zvečer je 16,7.
Sedaj najprej naredimo parametrični t-test.
t.test(podatki$grade_average~podatki$evening.attendanceF,
paired=FALSE,
var.equal=FALSE,
alternative="two.sided")##
## Welch Two Sample t-test
##
## data: podatki$grade_average by podatki$evening.attendanceF
## t = -3.8517, df = 597.33, p-value = 0.00013
## alternative hypothesis: true difference in means between group evening and group daytime is not equal to 0
## 95 percent confidence interval:
## -1.3868921 -0.4501859
## sample estimates:
## mean in group evening mean in group daytime
## 9.617258 10.535797Uporabili smo popravek za homogenost varianc, saj variance skoraj nikoli niso enake, je pa to zahtevek parametričnega testa skupin. P vrednost je manjša kot 0.05, zato lahko zavrnemo H0 in sprejmemo sklep, da se povprečna ocena med dnevnimi in nočnimi študenti razlikuje, p=0.00013. Da lahko zavrbemo H0 lahko vidimo tudi iz intervala zaupanja, ki ne vključuje t-statistike.
Študentje, ki fakulteto obiskujejo podevni imajo višjo povprečno oceno kot študentje, ki fakulteto obiskujejo zvečer.Zanima nas še, kako velik je učinek.
library(effectsize)##
## Attaching package: 'effectsize'## The following object is masked from 'package:psych':
##
## phi## The following objects are masked from 'package:rstatix':
##
## cohens_d, eta_squaredcohens_d(podatki$grade_average~podatki$evening.attendanceF,
pooled_sd = FALSE)## Cohen's d | 95% CI
## --------------------------
## -0.19 | [-0.28, -0.09]
##
## - Estimated using un-pooled SD.Učinek je zelo majhen (very small).
Sedaj naredimo še (bolj ustrezen) neparametrični test.
wilcox.test(podatki$grade_average~podatki$evening.attendanceF,
paired=FALSE,
correct=FALSE,
exact=FALSE,
alternative="two.sided")##
## Wilcoxon rank sum test
##
## data: podatki$grade_average by podatki$evening.attendanceF
## W = 760424, p-value = 4.669e-13
## alternative hypothesis: true location shift is not equal to 0H0 zavrnemo pri p<0.001 in sprejmemo sklep, da je lokacija porazdelitve povprečnih ocen pri študentih, ki fakulteto obiskujejo podnevi drugačna od lokacije porazdelitve povprečnih ocenih pri študentih, ki fakulteto obiskujejo zvečer.
library(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaggplot2::ggplot(podatki, aes(x=grade_average, fill=evening.attendanceF)) +
geom_histogram(position = position_dodge(width = 2.5), binwidth = 5, colour="Black") +
scale_x_continuous(breaks = seq(0,20,2)) +
ylab("Frekvenca") +
labs(fill="Prisotnost")
Graf ni najbolj informativen, saj sta velikosti vzorcev med skupinama zelo različni. Vseeno lahko vidimo, da imajo učenci, ki šolo obiskujejo podnevi boljše povprečne ocene od tistih, ki šolo obiskujejo zvečer.
effectsize(wilcox.test(podatki$grade_average~podatki$evening.attendanceF,
paired=FALSE,
correct=FALSE,
exact=FALSE,
alternative="two.sided"))## r (rank biserial) | 95% CI
## ----------------------------------
## -0.20 | [-0.25, -0.15]Velikost učinka je sedaj bolj obetavna, interpretiramo jo kot srednje veliko.
- Na enakih podatkih izvedemo še regresijo. Povprečno oceno študentov bomo napovedovali s spremenljivkami starost in spol. Predvidevamo, da bo starost pozitivno vplivala na povporečno oceno. Pogledali bomo ali se razlike spreminjajo, glede na spol osebe.
Najprej uredimo podatke.
podatki$GenderF <- factor(podatki$Gender,
levels = c(0,1),
labels = c("male", "female"))
head(podatki[,-c(13,14,15)])## Marital.status evening.attendance Educational.special.needs Gender
## 1 1 1 0 1
## 2 1 1 0 1
## 3 1 1 0 1
## 4 1 1 0 0
## 5 2 0 0 0
## 6 2 0 0 1
## Scholarship.holder Age.at.enrollment Curricular.units.1st.sem..grade.
## 1 0 20 0.00000
## 2 0 19 14.00000
## 3 0 19 0.00000
## 4 0 20 13.42857
## 5 0 45 12.33333
## 6 0 50 11.85714
## Curricular.units.2nd.sem..grade. grade_average evening.attendanceF GenderF
## 1 0.00000 0.00000 daytime female
## 2 13.66667 13.83333 daytime female
## 3 0.00000 0.00000 daytime female
## 4 12.40000 12.91429 daytime male
## 5 13.00000 12.66667 evening male
## 6 11.50000 11.67857 evening femaleLinearna regresijska funkcija, ki bomo ocenjevali: Grade_average = b0 + b1starost + b2spol + b3starostspol
Najprej preglejmo podatke
summary(podatki[c("grade_average", "GenderF", "Age.at.enrollment")])## grade_average GenderF Age.at.enrollment
## Min. : 0.00 male :2868 Min. :17.00
## 1st Qu.:11.00 female:1556 1st Qu.:19.00
## Median :12.25 Median :20.00
## Mean :10.44 Mean :23.27
## 3rd Qu.:13.27 3rd Qu.:25.00
## Max. :18.28 Max. :70.00Vidimo, da je v vzorcu več žensk kot moških. Skupna povprečna starost je 23,27 let, 95% vrednosti pa se nahaja med starostma 19 in 25 let. Najbolj star posameznik, ki je del vzorca ima 70 let.
describeBy(podatki$grade_average, podatki$Gender)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2868 11.16 4.27 12.46 12.07 1.53 0 17.36 17.36 -1.88 2.27 0.08
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1556 9.11 5.45 11.7 9.54 2.37 0 18.28 18.28 -0.86 -0.93 0.14Vidimo, da je povprečna ocena višja pri ženskah kot pri moški.
car::scatterplot(grade_average ~ Age.at.enrollment | GenderF,
ylab = "Povrecna ocena",
xlab = "Starost ob vpisu",
smooth=FALSE,
boxplots = FALSE,
data = podatki)
Naklona se razlikujeta, zato interkacija do neke vrste je prisotna. Spol
je umetna spremenljivka, bazna vrednost so moški, torej bomo ženske
primerjali z moškimi.
podatki_m <- podatki[podatki$GenderF == "male",]
podatki_z <- podatki[podatki$GenderF == "female",]
fit_m <- lm(grade_average ~ Age.at.enrollment,
data = podatki_m)
summary(fit_m)##
## Call:
## lm(formula = grade_average ~ Age.at.enrollment, data = podatki_m)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.610 0.138 1.238 2.242 7.450
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.45247 0.26455 50.850 <2e-16 ***
## Age.at.enrollment -0.10239 0.01126 -9.094 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.212 on 2866 degrees of freedom
## Multiple R-squared: 0.02804, Adjusted R-squared: 0.02771
## F-statistic: 82.69 on 1 and 2866 DF, p-value: < 2.2e-16Regresijska funkcija za moške: grade_average = 13.45 - 0.10*starost Če se starost poveča ze eno enoto (eno leto), povprečna ocena v povprečju pade za 0,1 enote. Vidimo lahko, da smo pojasnili zelo majhen del variance, le 2,8% variabilnosti povprečne ocene lahko pojasnimo s starostjo.
Enako storimo še za ženske (spodaj). Regresijska funkcija za ženske: grade_average = 11.08 - 0.08*starost Če se starost poveča ze eno enoto (eno leto), povprečna ocena v povprečju pade za 0,08 enote. Vidimo lahko, da smo pojasnili še manjši del variabilnosti, le 1,4% variabilnosti povprečne ocene lahko pojasnimo s starostjo.
fit_z <- lm(grade_average ~ Age.at.enrollment,
data = podatki_z)
summary(fit_z)##
## Call:
## lm(formula = grade_average ~ Age.at.enrollment, data = podatki_z)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.729 -3.947 2.491 3.682 9.748
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.08218 0.42865 25.85 < 2e-16 ***
## Age.at.enrollment -0.07959 0.01638 -4.86 1.29e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.409 on 1554 degrees of freedom
## Multiple R-squared: 0.01497, Adjusted R-squared: 0.01434
## F-statistic: 23.62 on 1 and 1554 DF, p-value: 1.293e-06fit <- lm(grade_average ~ Age.at.enrollment + GenderF + Age.at.enrollment:GenderF,
data = podatki)
summary(fit)##
## Call:
## lm(formula = grade_average ~ Age.at.enrollment + GenderF + Age.at.enrollment:GenderF,
## data = podatki)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.6095 -0.0904 1.5269 2.7596 9.7485
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.45247 0.29318 45.884 < 2e-16 ***
## Age.at.enrollment -0.10239 0.01248 -8.205 2.98e-16 ***
## GenderFfemale -2.37029 0.47203 -5.022 5.33e-07 ***
## Age.at.enrollment:GenderFfemale 0.02280 0.01885 1.209 0.227
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.668 on 4420 degrees of freedom
## Multiple R-squared: 0.06218, Adjusted R-squared: 0.06154
## F-statistic: 97.68 on 3 and 4420 DF, p-value: < 2.2e-16Regresijska funkcija: grade_average = 13.45 - 0.12starost - 2.37spol + 0.02starostspol Če se starost poveča za eno enoto, se povprečna ocena povprečno zmanjša za 0.12 enote. Interakcije ne interpretiramo, saj se ni izkazala za statistično značilno. Z modelom smo pojasnili le 6,2% variabilnosti povprečne ocene, kar je relativno malo. V model bi bilo potrebno vključiti več spremenljivk, ki imajo bolj pomemben vpliv na povprečno oceno kot sta starost in spol.
podatki$StdOstanki <- round(rstandard(fit),3)
podatki$CooksD <- round(cooks.distance(fit),3)
hist(podatki$StdOstanki,
xlab = "Standardizirani ostanki",
ylab = "Frekvenca",
main = "Histogram standardiziranih vrednosti")
Histogram standardiziranih vrednosti kaže na odstopanja od normalne
porazdelitve standardiziranih ostankov, ki so predpostavka za izvedbo
regresije.
hist(podatki$CooksD,
xlab = "Cookove razdalje",
ylab = "Frekvenca",
main = "Histogram Cookovih razdalij")
Vidimo določene točke z vplivom, ki jih bo potrebno odstraniti iz
analize.
head(podatki[order(podatki$StdOstanki), "StdOstanki"],5)## [1] -2.488 -2.488 -2.488 -2.488 -2.488head(podatki[order(-podatki$StdOstanki), "StdOstanki"],5)## [1] 2.090 1.971 1.906 1.836 1.780head(podatki[order(-podatki$CooksD), "CooksD"],10)## [1] 0.009 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.005 0.005podatkiC <- podatki[c(-708, -690, -2662, -726),]
shapiro.test(podatki$StdOstanki)##
## Shapiro-Wilk normality test
##
## data: podatki$StdOstanki
## W = 0.79794, p-value < 2.2e-16Odstranili smo točje z vplivom, porazdelitev standardiziranih ostankov odstopa od normalnosti, torej kršimo predpostavko regresije.
Še enkrat jo izvedemo, brez točk z vplivom.
fit2 <- lm(grade_average ~ Age.at.enrollment + GenderF + Age.at.enrollment:GenderF,
data = podatkiC)
summary(fit2)##
## Call:
## lm(formula = grade_average ~ Age.at.enrollment + GenderF + Age.at.enrollment:GenderF,
## data = podatkiC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.6095 -0.0904 1.5239 2.7577 9.7962
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.45247 0.29296 45.919 < 2e-16 ***
## Age.at.enrollment -0.10239 0.01247 -8.212 2.84e-16 ***
## GenderFfemale -2.26189 0.47697 -4.742 2.18e-06 ***
## Age.at.enrollment:GenderFfemale 0.01792 0.01909 0.938 0.348
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.664 on 4416 degrees of freedom
## Multiple R-squared: 0.06292, Adjusted R-squared: 0.06228
## F-statistic: 98.83 on 3 and 4416 DF, p-value: < 2.2e-16Regresijski koeficienti ostajajo praktično enaki, interakcija še vedno ni značilna.
podatkiC$StdOcenVred <- scale(fit2$fitted.values)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(StdOstanki~StdOcenVred,
ylab = "Standardizirani ostanki",
xlab = "Standardizirane ocenjene vrednosti",
smooth=FALSE,
regLine=FALSE,
boxplots=FALSE,
data = podatkiC)
Preverjamo še predpostavko o homoskedastičnosti. Vidimo, da variabilnost
ni konstantna, na grafu vidimo določene vzorce. Lahko bi predvidevali,
da gre za časovne vrste. Kršimo tudi predpostavko o homoskedastičnosti,
potrdimo to še s testom.
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversols_test_breusch_pagan(fit2)##
## Breusch Pagan Test for Heteroskedasticity
## -----------------------------------------
## Ho: the variance is constant
## Ha: the variance is not constant
##
## Data
## -----------------------------------------
## Response : grade_average
## Variables: fitted values of grade_average
##
## Test Summary
## -------------------------------
## DF = 1
## Chi2 = 208.0186
## Prob > Chi2 = 3.716663e-47Test je kot ptičakovano potrdil, da je predpostavka o homoskedastičnosti kršena. V tem primeru bi bilo podatke najbolj smiselno transformirati (npr. logaritmirati) oz. v regresijsko funkcijo vstaviti nove spremenljivke, obstoječe pa odstraniti, saj se vključene spremenljivke niso izkazale kot najbolj smiselne za našo analizo.