En una ingenio de café hacen la recepción de bultos de café de aproximadamente 60 Kg para llevarlos a procesamiento. Esté café debe cumplir el requerimiento en proporción de granos de maduros y grados verdes ya que la presencia de estos últimos afecta la calidad aromática del producto final. Al realizar el muestreo destructivo en un lote de 2000 bultos se encontraron las siguientes proporciones:

###Generacion de datos
set.seed(1073173761)
sample<-round(rbeta(2000,10,0.2),3);sample #proporcion de granos maduros
##    [1] 0.898 1.000 1.000 0.983 0.995 0.999 1.000 0.986 1.000 1.000 1.000
##   [12] 0.975 1.000 0.978 0.996 0.950 0.865 1.000 0.969 0.999 0.879 1.000
##   [23] 1.000 0.984 0.983 0.999 1.000 1.000 0.995 1.000 1.000 0.979 0.995
##   [34] 1.000 1.000 0.990 0.993 0.893 0.816 1.000 1.000 1.000 0.997 1.000
##   [45] 1.000 1.000 0.995 1.000 0.998 0.976 0.999 0.917 0.996 0.964 1.000
##   [56] 1.000 1.000 1.000 1.000 0.963 0.997 0.938 0.970 1.000 0.991 0.995
##   [67] 1.000 0.999 0.875 1.000 1.000 1.000 1.000 0.985 0.980 0.961 0.993
##   [78] 0.908 0.999 0.994 0.993 1.000 0.996 0.997 0.984 1.000 1.000 0.995
##   [89] 0.996 0.922 0.835 1.000 0.910 0.975 0.993 1.000 1.000 1.000 1.000
##  [100] 0.917 0.980 1.000 0.998 0.968 1.000 0.991 0.998 0.999 0.803 1.000
##  [111] 0.999 0.997 1.000 1.000 0.998 0.999 1.000 0.997 1.000 0.977 0.998
##  [122] 1.000 0.950 0.999 0.997 1.000 1.000 0.999 1.000 0.999 0.958 1.000
##  [133] 0.935 0.998 0.960 0.835 1.000 0.998 0.921 0.983 0.999 1.000 1.000
##  [144] 0.979 0.867 1.000 0.984 1.000 1.000 0.986 1.000 0.994 1.000 0.999
##  [155] 0.970 0.999 1.000 0.998 0.929 0.975 0.961 1.000 0.997 0.999 1.000
##  [166] 0.970 0.996 0.999 0.977 0.999 0.952 0.999 1.000 0.991 1.000 0.988
##  [177] 0.997 0.932 0.981 0.997 0.988 1.000 0.984 0.999 0.999 1.000 0.975
##  [188] 0.964 0.998 0.885 0.917 0.985 0.944 1.000 1.000 0.958 0.991 0.991
##  [199] 0.949 1.000 0.987 0.994 0.970 1.000 1.000 1.000 0.815 0.999 0.938
##  [210] 1.000 0.983 1.000 0.999 0.987 0.999 0.970 1.000 0.998 0.848 0.985
##  [221] 0.957 1.000 0.920 1.000 1.000 0.744 0.999 1.000 0.994 0.998 0.992
##  [232] 1.000 0.996 1.000 1.000 0.981 1.000 1.000 0.992 0.999 1.000 0.981
##  [243] 0.993 0.931 0.984 0.991 0.978 0.991 0.921 1.000 1.000 0.998 0.994
##  [254] 0.970 0.976 0.998 0.970 0.986 1.000 1.000 0.997 0.983 1.000 1.000
##  [265] 0.955 0.990 0.923 1.000 1.000 0.913 0.968 1.000 0.921 0.999 0.987
##  [276] 0.992 1.000 0.991 0.939 0.977 1.000 0.997 0.999 0.767 0.864 0.943
##  [287] 0.999 0.965 1.000 0.999 1.000 1.000 1.000 0.983 1.000 1.000 1.000
##  [298] 0.970 1.000 0.979 1.000 0.997 0.990 0.975 1.000 1.000 0.945 1.000
##  [309] 1.000 0.968 1.000 0.959 1.000 0.999 0.997 1.000 0.926 0.998 0.997
##  [320] 1.000 0.918 0.973 0.994 0.953 0.996 0.998 0.929 1.000 0.976 1.000
##  [331] 0.992 0.999 0.847 0.985 1.000 1.000 0.994 0.958 1.000 0.976 1.000
##  [342] 1.000 0.999 1.000 1.000 0.994 0.983 0.994 0.999 0.997 0.994 0.942
##  [353] 1.000 1.000 0.999 1.000 0.983 0.964 1.000 0.998 0.733 0.972 0.994
##  [364] 0.959 0.999 1.000 1.000 1.000 0.937 1.000 0.997 1.000 0.985 0.999
##  [375] 0.999 0.988 0.989 0.999 1.000 0.996 0.999 1.000 0.996 0.998 0.999
##  [386] 1.000 0.967 0.958 1.000 0.990 1.000 0.977 0.994 0.937 0.997 0.913
##  [397] 1.000 1.000 0.994 0.975 1.000 0.996 0.987 0.997 1.000 0.928 0.987
##  [408] 1.000 0.969 0.975 1.000 0.993 1.000 0.998 0.998 0.838 0.997 1.000
##  [419] 1.000 1.000 0.983 1.000 0.998 0.946 1.000 1.000 0.975 0.997 0.992
##  [430] 1.000 0.999 1.000 0.948 0.996 0.994 0.998 0.979 1.000 0.939 0.998
##  [441] 0.993 0.972 1.000 0.999 0.984 1.000 0.995 0.999 1.000 0.996 0.993
##  [452] 0.686 0.977 1.000 0.966 1.000 1.000 1.000 1.000 0.982 1.000 0.970
##  [463] 0.949 0.999 0.999 0.995 0.998 1.000 1.000 0.999 1.000 1.000 0.972
##  [474] 1.000 1.000 1.000 1.000 0.996 0.914 1.000 0.985 0.953 1.000 1.000
##  [485] 0.977 0.957 1.000 0.999 0.985 1.000 0.972 0.869 0.999 0.991 1.000
##  [496] 0.986 0.974 0.995 1.000 0.994 0.996 0.930 0.777 1.000 0.983 0.975
##  [507] 0.931 1.000 0.999 1.000 0.961 0.994 1.000 0.994 0.971 1.000 0.988
##  [518] 1.000 1.000 0.981 0.960 1.000 1.000 0.984 1.000 0.979 0.924 0.998
##  [529] 0.969 0.978 1.000 0.991 0.992 0.972 0.990 1.000 1.000 0.984 0.999
##  [540] 0.986 1.000 1.000 1.000 0.929 0.953 1.000 0.981 1.000 0.993 0.868
##  [551] 0.994 1.000 0.978 0.805 1.000 0.952 0.997 0.999 1.000 0.999 0.986
##  [562] 0.969 1.000 1.000 1.000 1.000 0.997 0.921 1.000 1.000 0.981 0.993
##  [573] 0.986 0.905 0.996 0.999 0.997 0.906 0.985 0.997 0.998 0.995 0.992
##  [584] 0.996 0.996 1.000 0.994 0.996 1.000 0.985 0.998 0.981 1.000 1.000
##  [595] 0.931 0.984 0.998 1.000 1.000 0.976 0.655 1.000 0.991 0.986 1.000
##  [606] 1.000 0.999 1.000 0.998 0.999 0.996 0.999 1.000 0.989 1.000 0.970
##  [617] 0.999 0.994 0.997 1.000 0.999 0.997 1.000 0.973 0.993 1.000 0.998
##  [628] 1.000 0.999 0.985 0.999 0.944 0.998 0.998 0.951 0.995 0.985 1.000
##  [639] 0.996 1.000 0.998 0.999 0.984 1.000 0.997 1.000 0.979 1.000 0.995
##  [650] 1.000 0.996 0.998 0.920 0.997 1.000 0.999 0.960 0.878 0.999 0.925
##  [661] 0.992 1.000 0.999 1.000 0.999 1.000 0.997 0.993 0.996 0.999 1.000
##  [672] 1.000 0.985 0.971 0.958 0.995 0.999 0.986 1.000 0.986 1.000 0.999
##  [683] 0.941 1.000 0.988 0.999 0.992 1.000 1.000 0.985 1.000 0.989 1.000
##  [694] 0.971 0.997 0.996 0.968 1.000 1.000 0.957 0.953 0.922 0.961 0.999
##  [705] 1.000 1.000 0.998 0.998 1.000 1.000 1.000 1.000 1.000 0.980 0.993
##  [716] 1.000 0.999 0.991 1.000 0.958 1.000 0.978 0.959 1.000 1.000 1.000
##  [727] 0.985 1.000 0.938 0.938 0.773 0.962 0.999 0.993 1.000 1.000 1.000
##  [738] 1.000 0.942 0.999 0.996 0.989 1.000 0.992 0.841 0.984 1.000 0.984
##  [749] 1.000 1.000 1.000 0.878 0.996 0.999 1.000 1.000 0.984 0.993 0.998
##  [760] 0.883 1.000 0.939 0.989 0.985 1.000 0.969 0.997 0.999 0.979 1.000
##  [771] 0.968 0.996 0.988 1.000 0.998 0.998 0.960 0.993 1.000 0.938 0.942
##  [782] 0.992 1.000 0.999 1.000 0.943 0.943 0.975 0.995 0.966 0.978 1.000
##  [793] 0.984 0.994 1.000 0.988 1.000 0.973 0.999 0.999 0.999 1.000 0.987
##  [804] 1.000 0.966 0.899 0.983 0.989 0.982 0.981 0.999 1.000 0.940 0.995
##  [815] 1.000 0.981 1.000 1.000 0.991 1.000 0.987 0.991 1.000 0.997 0.995
##  [826] 1.000 1.000 1.000 1.000 0.991 0.879 0.712 1.000 1.000 0.997 0.984
##  [837] 0.965 1.000 1.000 0.985 0.928 0.998 0.988 0.985 0.965 1.000 0.999
##  [848] 1.000 1.000 1.000 0.998 0.949 1.000 0.871 1.000 0.936 0.967 0.996
##  [859] 1.000 1.000 1.000 1.000 1.000 0.943 0.997 1.000 1.000 0.943 0.990
##  [870] 0.899 1.000 0.992 1.000 0.983 0.950 0.999 1.000 0.999 0.973 0.998
##  [881] 0.999 0.998 1.000 0.998 0.982 1.000 1.000 0.998 1.000 1.000 1.000
##  [892] 0.998 1.000 0.818 0.998 0.989 0.995 0.996 1.000 0.981 0.991 0.988
##  [903] 0.973 1.000 1.000 0.980 0.998 0.991 1.000 0.996 1.000 0.938 0.911
##  [914] 1.000 0.975 1.000 1.000 1.000 0.999 0.920 0.956 0.768 0.977 1.000
##  [925] 1.000 0.991 0.999 1.000 0.999 1.000 0.994 0.996 1.000 1.000 0.882
##  [936] 0.922 1.000 1.000 1.000 0.996 0.996 0.980 0.992 0.982 1.000 1.000
##  [947] 0.999 0.998 0.929 1.000 0.990 0.996 1.000 0.997 1.000 0.967 0.999
##  [958] 0.880 0.997 1.000 1.000 0.984 1.000 0.973 1.000 1.000 0.946 0.957
##  [969] 1.000 0.992 1.000 0.968 0.992 1.000 1.000 0.961 1.000 0.951 0.987
##  [980] 1.000 0.985 0.998 1.000 0.972 0.807 0.986 1.000 0.987 0.932 0.874
##  [991] 0.987 1.000 1.000 1.000 1.000 0.906 1.000 0.917 1.000 0.991 0.965
## [1002] 0.944 1.000 0.986 1.000 0.917 0.997 0.974 0.999 1.000 0.996 0.992
## [1013] 0.988 0.999 0.960 0.997 1.000 1.000 1.000 0.994 0.984 1.000 1.000
## [1024] 0.995 0.975 1.000 0.999 0.997 1.000 1.000 1.000 0.998 0.964 1.000
## [1035] 0.920 0.993 1.000 1.000 1.000 1.000 0.991 0.982 0.977 0.978 1.000
## [1046] 0.975 1.000 1.000 1.000 0.998 0.985 0.996 1.000 0.953 1.000 0.971
## [1057] 0.990 1.000 0.983 0.998 1.000 0.997 0.994 0.983 0.943 0.996 0.995
## [1068] 1.000 1.000 0.999 1.000 1.000 0.995 0.965 0.995 0.795 1.000 0.994
## [1079] 1.000 1.000 0.973 1.000 1.000 0.990 0.999 1.000 1.000 0.974 0.953
## [1090] 0.998 1.000 1.000 0.998 0.991 0.953 0.999 0.991 0.991 0.984 1.000
## [1101] 0.992 0.999 0.969 0.872 0.931 0.986 0.998 0.999 0.997 0.987 1.000
## [1112] 0.882 0.857 1.000 0.995 1.000 0.966 0.749 1.000 1.000 0.970 1.000
## [1123] 0.998 0.987 0.820 0.996 1.000 0.996 0.998 1.000 1.000 1.000 1.000
## [1134] 0.999 0.904 1.000 1.000 1.000 0.996 0.984 0.835 1.000 0.962 0.956
## [1145] 0.998 0.981 1.000 0.978 1.000 1.000 0.830 0.999 0.993 0.993 0.996
## [1156] 0.999 0.990 1.000 1.000 0.985 1.000 0.993 0.951 1.000 1.000 0.994
## [1167] 1.000 0.898 0.970 0.954 0.999 0.982 0.993 0.991 0.986 1.000 1.000
## [1178] 1.000 0.998 1.000 0.967 0.995 0.973 1.000 0.955 0.978 0.998 0.989
## [1189] 1.000 0.946 0.976 1.000 1.000 1.000 0.980 1.000 0.998 0.986 0.950
## [1200] 0.999 0.982 0.991 0.972 0.981 0.806 0.997 0.993 1.000 0.999 0.993
## [1211] 0.870 1.000 1.000 0.976 1.000 0.899 0.968 0.960 0.989 1.000 1.000
## [1222] 1.000 0.992 1.000 1.000 1.000 1.000 0.994 0.998 0.991 1.000 1.000
## [1233] 0.970 0.925 1.000 0.997 0.997 1.000 0.982 0.986 0.900 0.995 1.000
## [1244] 1.000 0.912 1.000 1.000 0.999 0.999 0.978 1.000 0.993 1.000 0.998
## [1255] 0.793 0.998 0.999 0.998 0.991 0.991 0.923 0.920 1.000 0.827 0.999
## [1266] 0.994 1.000 0.998 0.994 0.996 0.984 0.999 0.986 0.940 0.996 1.000
## [1277] 1.000 0.999 1.000 1.000 0.992 0.997 1.000 1.000 1.000 0.960 0.995
## [1288] 0.865 1.000 0.980 1.000 0.995 0.997 1.000 1.000 1.000 0.698 0.953
## [1299] 1.000 1.000 0.985 0.983 0.950 0.999 1.000 0.987 0.999 1.000 0.987
## [1310] 0.932 1.000 1.000 0.978 1.000 0.997 0.980 0.967 0.996 0.999 0.988
## [1321] 0.998 0.999 1.000 0.993 1.000 1.000 0.911 0.999 0.997 1.000 1.000
## [1332] 0.980 1.000 1.000 0.997 0.998 0.927 1.000 1.000 0.933 0.992 0.973
## [1343] 1.000 0.988 1.000 0.914 1.000 1.000 0.981 0.999 0.915 1.000 0.996
## [1354] 1.000 0.992 0.996 0.996 1.000 1.000 1.000 0.999 0.953 0.999 1.000
## [1365] 0.917 1.000 1.000 0.965 0.975 0.963 1.000 0.993 0.856 1.000 0.980
## [1376] 1.000 1.000 1.000 0.912 0.990 1.000 0.992 1.000 0.989 1.000 0.960
## [1387] 1.000 1.000 1.000 1.000 0.987 0.967 1.000 1.000 1.000 0.976 1.000
## [1398] 1.000 1.000 0.999 0.990 0.943 1.000 0.986 1.000 1.000 1.000 0.979
## [1409] 0.996 1.000 0.998 1.000 0.997 0.972 0.993 0.999 1.000 1.000 0.997
## [1420] 1.000 0.997 1.000 0.950 0.998 1.000 1.000 0.994 0.988 1.000 0.981
## [1431] 0.908 0.981 0.999 0.971 0.975 0.994 0.997 0.946 0.988 0.988 1.000
## [1442] 0.977 0.848 1.000 0.999 0.995 1.000 0.998 0.977 0.978 1.000 0.946
## [1453] 0.789 0.982 1.000 1.000 1.000 0.874 0.984 1.000 0.975 1.000 0.999
## [1464] 1.000 0.982 1.000 1.000 0.868 0.995 0.998 0.993 1.000 1.000 0.999
## [1475] 1.000 0.890 0.999 1.000 0.981 0.992 1.000 0.994 0.993 1.000 0.998
## [1486] 1.000 1.000 1.000 0.999 0.947 0.984 0.999 0.962 0.999 0.966 1.000
## [1497] 0.999 1.000 1.000 1.000 0.987 0.999 1.000 0.998 0.992 1.000 1.000
## [1508] 0.999 0.997 0.987 0.993 0.989 0.999 0.986 0.995 1.000 0.991 1.000
## [1519] 1.000 0.999 1.000 0.998 1.000 0.999 0.998 0.994 1.000 0.999 0.997
## [1530] 0.963 1.000 0.965 1.000 1.000 0.999 0.996 0.999 0.725 1.000 0.995
## [1541] 0.998 1.000 1.000 0.980 1.000 0.914 1.000 0.998 0.946 1.000 0.992
## [1552] 1.000 0.998 0.999 0.978 1.000 0.998 1.000 0.906 0.987 1.000 0.987
## [1563] 0.831 1.000 1.000 0.999 1.000 0.966 1.000 0.992 1.000 0.864 0.999
## [1574] 0.956 1.000 1.000 0.984 1.000 0.929 0.989 0.998 0.947 0.954 0.996
## [1585] 0.999 0.995 1.000 0.979 1.000 0.999 1.000 1.000 0.998 0.967 1.000
## [1596] 1.000 1.000 0.921 0.925 0.861 1.000 0.874 0.991 1.000 1.000 1.000
## [1607] 1.000 0.999 1.000 0.963 0.999 1.000 0.977 0.997 0.967 0.998 0.970
## [1618] 1.000 1.000 0.989 1.000 0.991 1.000 1.000 0.966 0.975 1.000 0.982
## [1629] 1.000 1.000 1.000 1.000 0.963 1.000 1.000 1.000 0.925 1.000 0.999
## [1640] 1.000 1.000 1.000 0.993 0.971 0.996 0.939 1.000 0.998 0.716 1.000
## [1651] 0.996 1.000 0.972 1.000 0.954 1.000 0.993 1.000 0.904 0.981 1.000
## [1662] 0.998 1.000 0.978 1.000 1.000 0.994 1.000 0.997 0.910 1.000 0.999
## [1673] 0.937 0.977 0.980 0.997 1.000 1.000 0.995 0.734 0.993 0.945 0.965
## [1684] 0.876 0.982 0.967 0.903 1.000 1.000 1.000 0.997 0.999 1.000 0.998
## [1695] 0.958 0.955 0.999 0.998 0.979 1.000 0.999 0.992 1.000 1.000 1.000
## [1706] 0.999 1.000 1.000 1.000 0.980 0.999 1.000 0.996 1.000 1.000 1.000
## [1717] 0.657 1.000 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.790
## [1728] 0.970 0.985 0.996 1.000 0.867 0.993 1.000 0.993 1.000 0.992 0.999
## [1739] 0.999 1.000 1.000 0.883 0.941 1.000 0.992 0.979 0.990 1.000 0.987
## [1750] 1.000 0.995 0.963 0.979 1.000 0.977 1.000 0.984 1.000 1.000 0.965
## [1761] 1.000 1.000 1.000 0.990 0.982 1.000 1.000 0.866 0.922 0.997 1.000
## [1772] 0.990 1.000 0.992 1.000 0.998 0.987 0.870 0.955 1.000 0.980 1.000
## [1783] 0.999 1.000 1.000 0.999 1.000 1.000 1.000 0.988 0.962 0.997 1.000
## [1794] 0.936 0.956 1.000 0.998 0.992 1.000 0.980 0.993 0.998 1.000 0.962
## [1805] 0.996 0.930 0.970 0.991 0.987 1.000 0.999 1.000 1.000 0.980 1.000
## [1816] 0.971 0.880 0.991 0.998 1.000 0.895 0.965 0.928 0.994 0.999 1.000
## [1827] 0.999 1.000 0.894 1.000 1.000 0.994 0.997 1.000 1.000 0.986 1.000
## [1838] 0.991 1.000 1.000 1.000 1.000 0.990 1.000 0.861 0.988 1.000 0.985
## [1849] 0.990 0.980 1.000 1.000 1.000 0.942 1.000 1.000 0.967 0.982 0.999
## [1860] 0.768 1.000 1.000 1.000 1.000 0.970 1.000 1.000 0.973 1.000 1.000
## [1871] 1.000 0.991 0.973 0.995 1.000 1.000 0.999 0.898 1.000 0.974 0.981
## [1882] 1.000 1.000 0.948 0.975 0.996 1.000 0.758 0.999 0.733 0.996 0.995
## [1893] 0.974 0.937 0.999 1.000 1.000 0.922 0.987 0.992 0.996 1.000 1.000
## [1904] 0.998 0.991 0.927 0.710 0.994 1.000 0.991 0.994 1.000 1.000 0.999
## [1915] 1.000 0.971 0.995 0.887 0.998 0.923 1.000 1.000 0.996 0.981 1.000
## [1926] 0.992 0.967 0.977 0.976 0.997 1.000 1.000 0.992 0.982 0.937 0.994
## [1937] 0.992 1.000 0.990 1.000 0.976 0.994 0.996 0.941 0.999 1.000 0.993
## [1948] 1.000 0.999 0.970 1.000 0.919 0.998 0.686 1.000 0.983 0.975 0.955
## [1959] 1.000 1.000 1.000 0.999 0.988 1.000 0.999 0.989 0.999 1.000 0.999
## [1970] 1.000 0.999 0.999 1.000 0.999 0.996 0.981 1.000 0.992 0.983 1.000
## [1981] 1.000 0.986 0.996 0.999 0.962 1.000 1.000 0.999 0.980 0.998 1.000
## [1992] 0.983 0.994 1.000 0.910 0.999 1.000 0.984 0.981 0.995

Luego de recopilados los datos del muestreo, se procedió a estimar algunas estadísticas:

Estadísticas

minsample<-min(sample); minsample # Minimo
## [1] 0.655
maxsample<-max(sample); maxsample # Maximo
## [1] 1
meansample<-mean(sample);meansample # Media
## [1] 0.981465
medsample<- median(sample);medsample # Mediana
## [1] 0.998
sdsample<-sd(sample); sdsample # Desviacion estandar
## [1] 0.04028085
varsample<- var(sample); varsample # Varianza
## [1] 0.001622547
qusample<- quantile(sample,c(0.2,0.25,0.75,0.8));qusample # Cuartiles y percentiles:
##   20%   25%   75%   80% 
## 0.975 0.982 1.000 1.000
qu1sample<-qusample[2];qu1sample # C. inferior
##   25% 
## 0.982
qu3sample<-qusample[3];qu3sample # C. superior
## 75% 
##   1
qu20<-qusample[1];qu20 # percentil 20%
##   20% 
## 0.975
qu80<-qusample[4];qu80 # percentil 80%
## 80% 
##   1

Posteriormente, para observar cual era el comportamiento en la distribución de los datos, se construyó el siguiente histograma:

Hmuestra<-hist(sample,col="darkred",main = "Calidad de los granos de cafe",xlab = "Proporcion de granos maduros por saco", ylab= "Frecuencia")
abline(v=meansample,col="green",lwd=4)
abline(v=medsample,col="aquamarine3",lwd=4)
abline(v=qu1sample,col="purple",lwd=4)
abline(v=qu3sample,col="blue",lwd=4)
abline(v=qu20,col="cornflowerblue",lwd=4)
abline(v=qu80,col="chartreuse4",lwd=4)

Al ubicar los valores de la media, la mediana, los cuartiles y los percentiles se puede apreciar a primera vista que aparentemente todas las anteriores son igualmente representativas. Sin embargo, al realizar un ajuste en el histograma y disminuir el tamaño de los intervalos se puede observar lo siguiente:

Hmuestra<-hist(sample,col="darkred",main = "Calidad de los granos de cafe",xlab = "Proporcion de granos maduros por saco", ylab= "Frecuencia", breaks = 30,xlim = c(0.9,1))
abline(v=meansample,col="green",lwd=4)
abline(v=medsample,col="aquamarine3",lwd=4)
abline(v=qu1sample,col="purple",lwd=4)
abline(v=qu3sample,col="blue",lwd=4)
abline(v=qu20,col="cornflowerblue",lwd=4)
abline(v=qu80,col="chartreuse4",lwd=4)

De esta manera se logra apreciar que las estadísticas estimadas anteriormente pueden ser representativas en la medida en que los intervalos en los que se encuentren sean de mayor o menor tamaño. A partir de esto, es posible afirmar que tanto los percentiles 75% y 80% como la mediana son los valores que representan en mayor proporción a la población muestreada.

Ahora, teninendo en cuenta las estadísticas estimadas anteriormente, se determinaran las probabilidades de que el producto sea penalizado partiendo de la siguiente tabla suministrada por el ingenio:

%Granos verdes %Penalización
[0-10) 0
[10-20) 12
[20-50) 60
[50-100] Devolución

Estimacion de probabilidades

Basado en el promedio:

100*table(0.5<=meansample & meansample<1)/length(sample)
## 
## TRUE 
## 0.05

Basado en la mediana:

100*table(0<=medsample & medsample<0.1)/length(sample)
## 
## FALSE 
##  0.05

Basado en el cuartil 1:

100*table(0<=qu1sample & qu1sample<0.1)/length(sample)
## 
## FALSE 
##  0.05

Basado en el cuartil 3:

100*table(0.2<=qu3sample & qu3sample<0.5)/length(sample)
## 
## FALSE 
##  0.05

Porcentaje de bultos que tienen a lo sumo 18% de granos verdes:

100*sum(0.18<=(1-sample))/length(sample)
## [1] 1.6

Porcentaje de sacos que tienen mínimo 5% de granos verdes:

100*sum(0.05>=(1-sample))/length(sample)
## [1] 88.95

Boxplot

boxplot(sample, col="darkgoldenrod2", main="Calidad de los granos de cafe", horizontal = T, ylim=c(0.85,1),xlab="Proporcion de granos maduros")
arrows(x0=0.9,y0=1.5, x1=0.9, y1= 0.5,lwd = 3,lty = 3)
text(0.8725,0.65,"Zona de penalizacion",col = "red")
lineas<-sort(c(medsample,meansample,qu1sample,qu20,qu3sample,qu80),decreasing = F)
abline(v=lineas,col=c("blue","deepskyblue3","blueviolet","darkmagenta","red","red"),lwd=3)
text((qu20-0.005),1.4,expression(x[20]),col="blue")
text((qu20-0.005),1.35,expression((0.975)),col="blue",cex = 0.5)
text((meansample-0.0025),1.41,expression(bar(x)),col="deepskyblue3")
text((meansample-0.0031),1.35,expression((0.98)),col="deepskyblue3",cex = 0.5)
text((qu1sample+0.0049),1.4,expression(x[25]),col="blueviolet")
text((qu1sample+0.0049),1.35,expression((0.982)),col="blueviolet",cex=0.5)
text((medsample-0.0025),1.425,expression(hat(x)),col="darkmagenta")
text((medsample-0.0029),1.35,expression((0.998)),col="darkmagenta",cex = 0.5)
text((qu3sample+0.0032),1.4,expression(x[75]),col="red",cex = 0.75)
text((qu3sample+0.0032),1.45,expression(x[80]),col="red",cex = 0.75)
text((qu3sample+0.0032),1.35,expression((1)),col="red",cex = 0.5)

Costo de recepción de los bultos de café luego de aplicar la penalización de los precios por su proporción de granos de café verde:

sp<-(sum((1-sample)<=0.1)*100000);sp
## [1] 191200000
p12<-(sum((1-sample)<=0.2 & (1-sample)>0.1)*100000*0.88);p12
## [1] 5632000
p60<-(sum((1-sample)<=0.5 & (1-sample)>0.2)*100000*0.4);p60
## [1] 960000
dev<-(sum((1-sample)<=1 & (1-sample)>0.5)*0);dev
## [1] 0
costo_total_recepcion<-sp+p12+p60+dev;costo_total_recepcion
## [1] 197792000