Clases de los promedios de los alumnos del ITD
Objetivo: Determinar clases conforme reglas Sturges, Scott y FD (Freedman-Diaconis). Histograma y pastel
Proceso:
- Importar datos de promedios de alumnos
- Graficas histograma sin cortes o breaks
- Graficar histograma de alumnos con promedio mayor que cero. Sturges, Scott, FD
- Determinar clases conforme a Sturges
- Graficar pastel
- Determinar clases conforme a Scott
- Graficar pastel
- Determinar clases conforme a FD
- Graficar pastel
- Interpretar salidas de datos
Los datos
datos <- read.csv("C:/Users/SATELLITE/Documents/SEMESTRE ene-jun 2018/Z PROBABILIDAD Y ESTADISTICAS/DATOS/ALUMNOS DE ISC INSCRITOS/alumnos inscritos ene-jun 2018.csv", header = TRUE, sep = ",")
# datos # Los datos le ponemos comentario # para que no aparezcan son muchos
head(datos) # solo los primeros
## no semetre promedio carrera
## 1 1 7 82.27 ARQUITECTURA
## 2 2 11 82.59 ARQUITECTURA
## 3 3 8 87.47 ARQUITECTURA
## 4 4 12 83.18 ARQUITECTURA
## 5 5 11 83.72 ARQUITECTURA
## 6 6 4 90.11 ARQUITECTURA
n.todos <- length(datos$promedio) # todos los datos
n.prom.mayor.cero <- length(datos$promedio[which(datos$promedio>0)])
n.todos # Cantidad total
## [1] 5946
n.prom.mayor.cero # Los que tienen promedio mayor que cero es la n que interesa
## [1] 5363
El histograma de los datos. Con frecuencia y cortes Sturges
El histograma sin cortes sales igual que el histograma de Sturges
El histograma de Scott sale igual que Freedman
hist(datos$promedio[which(datos$promedio > 0)], freq = TRUE, main = "Promedios mayores que cero de los alumnos inscritos del ITD", xlab = "Promedios", ylab = "Frecuencia")
hist(datos$promedio[which(datos$promedio > 0)], breaks = "Sturges", freq = TRUE, main = "Promedios mayores que cero de los alumnos inscritos del ITD", xlab = "Promedios", ylab = "Frecuencia")
hist(datos$promedio[which(datos$promedio > 0)], breaks = "Scott", freq = TRUE, main = "Promedios mayores que cero de los alumnos inscritos del ITD", xlab = "Promedios", ylab = "Frecuencia")
hist(datos$promedio[which(datos$promedio > 0)], breaks = "FD", freq = TRUE, main = "Promedios mayores que cero de los alumnos inscritos del ITD", xlab = "Promedios", ylab = "Frecuencia")
Determinando las frecuencias por clases (cortes). Los intervalos de clases. Sturges
# 1 + 3.33 * log10 ( n ) Fórmula de Sturges para número de clase
clases <- nclass.Sturges(datos$promedio[which(datos$promedio > 0)])
clases
## [1] 14
tabla.intervalos <- transform(table(cut(datos$promedio[which(datos$promedio > 0 )], breaks = clases)))
tabla.intervalos # es un data.frame
## Var1 Freq
## 1 (70,72.1] 5
## 2 (72.1,74.2] 5
## 3 (74.2,76.3] 36
## 4 (76.3,78.3] 195
## 5 (78.3,80.4] 572
## 6 (80.4,82.5] 927
## 7 (82.5,84.6] 974
## 8 (84.6,86.7] 855
## 9 (86.7,88.8] 685
## 10 (88.8,90.8] 522
## 11 (90.8,92.9] 339
## 12 (92.9,95] 181
## 13 (95,97.1] 51
## 14 (97.1,99.2] 16
# Podemos agregar columnas al Data.Frame. Frecuencia Relativa y Frecuencia Porcentual
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Rel' = tabla.intervalos$Freq / n.prom.mayor.cero)
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Porc' = tabla.intervalos$Freq.Rel * 100)
tabla.intervalos
## Var1 Freq Freq.Rel Freq.Porc
## 1 (70,72.1] 5 0.000932314 0.0932314
## 2 (72.1,74.2] 5 0.000932314 0.0932314
## 3 (74.2,76.3] 36 0.006712661 0.6712661
## 4 (76.3,78.3] 195 0.036360246 3.6360246
## 5 (78.3,80.4] 572 0.106656722 10.6656722
## 6 (80.4,82.5] 927 0.172851016 17.2851016
## 7 (82.5,84.6] 974 0.181614768 18.1614768
## 8 (84.6,86.7] 855 0.159425695 15.9425695
## 9 (86.7,88.8] 685 0.127727018 12.7727018
## 10 (88.8,90.8] 522 0.097333582 9.7333582
## 11 (90.8,92.9] 339 0.063210889 6.3210889
## 12 (92.9,95] 181 0.033749767 3.3749767
## 13 (95,97.1] 51 0.009509603 0.9509603
## 14 (97.1,99.2] 16 0.002983405 0.2983405
Haciendo un pastel de esta tabla de intervalos
Primero las etiquetas que son las clases y sus rangos
Luego las frecuencias en el pastel
# install.packages("plotrix")
library(plotrix)
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(tabla.intervalos$Freq, " Q de ", tabla.intervalos$Var1)
# recordar que n.prom.mayor.cero
# es la cantidad de alumnos con promedio mayor que cero
pie3D(tabla.intervalos$Freq, labels = etiquetas, main = paste("Frecuencia de clases. ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
# En porcentaje %
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(round(tabla.intervalos$Freq.Porc,2), " % de ", tabla.intervalos$Var1)
pie3D(round(tabla.intervalos$Freq.Porc,2), labels = etiquetas, main = paste("Frecuencia de clases. % ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
Determinando las frecuencias por clases (cortes). Los intervalos de clases. Scott
# 3.5 * s * n elevada a la (1/3)
# s es desviación std
clases <- nclass.scott(datos$promedio[which(datos$promedio > 0)])
clases
## [1] 34
tabla.intervalos <- transform(table(cut(datos$promedio[which(datos$promedio > 0 )], breaks = clases)))
tabla.intervalos # es un data.frame
## Var1 Freq
## 1 (70,70.9] 3
## 2 (70.9,71.7] 2
## 3 (71.7,72.6] 1
## 4 (72.6,73.4] 3
## 5 (73.4,74.3] 2
## 6 (74.3,75.1] 10
## 7 (75.1,76] 19
## 8 (76,76.9] 29
## 9 (76.9,77.7] 80
## 10 (77.7,78.6] 143
## 11 (78.6,79.4] 217
## 12 (79.4,80.3] 255
## 13 (80.3,81.2] 341
## 14 (81.2,82] 391
## 15 (82,82.9] 411
## 16 (82.9,83.7] 397
## 17 (83.7,84.6] 410
## 18 (84.6,85.4] 383
## 19 (85.4,86.3] 341
## 20 (86.3,87.2] 318
## 21 (87.2,88] 267
## 22 (88,88.9] 267
## 23 (88.9,89.7] 225
## 24 (89.7,90.6] 201
## 25 (90.6,91.4] 162
## 26 (91.4,92.3] 157
## 27 (92.3,93.2] 109
## 28 (93.2,94] 83
## 29 (94,94.9] 60
## 30 (94.9,95.7] 40
## 31 (95.7,96.6] 17
## 32 (96.6,97.5] 9
## 33 (97.5,98.3] 5
## 34 (98.3,99.2] 5
# Podemos agregar columnas al Data.Frame. Frecuencia Relativa y Frecuencia Porcentual
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Rel' = tabla.intervalos$Freq / n.prom.mayor.cero)
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Porc' = tabla.intervalos$Freq.Rel * 100)
tabla.intervalos
## Var1 Freq Freq.Rel Freq.Porc
## 1 (70,70.9] 3 0.0005593884 0.05593884
## 2 (70.9,71.7] 2 0.0003729256 0.03729256
## 3 (71.7,72.6] 1 0.0001864628 0.01864628
## 4 (72.6,73.4] 3 0.0005593884 0.05593884
## 5 (73.4,74.3] 2 0.0003729256 0.03729256
## 6 (74.3,75.1] 10 0.0018646280 0.18646280
## 7 (75.1,76] 19 0.0035427932 0.35427932
## 8 (76,76.9] 29 0.0054074212 0.54074212
## 9 (76.9,77.7] 80 0.0149170241 1.49170241
## 10 (77.7,78.6] 143 0.0266641805 2.66641805
## 11 (78.6,79.4] 217 0.0404624277 4.04624277
## 12 (79.4,80.3] 255 0.0475480142 4.75480142
## 13 (80.3,81.2] 341 0.0635838150 6.35838150
## 14 (81.2,82] 391 0.0729069551 7.29069551
## 15 (82,82.9] 411 0.0766362111 7.66362111
## 16 (82.9,83.7] 397 0.0740257319 7.40257319
## 17 (83.7,84.6] 410 0.0764497483 7.64497483
## 18 (84.6,85.4] 383 0.0714152527 7.14152527
## 19 (85.4,86.3] 341 0.0635838150 6.35838150
## 20 (86.3,87.2] 318 0.0592951706 5.92951706
## 21 (87.2,88] 267 0.0497855678 4.97855678
## 22 (88,88.9] 267 0.0497855678 4.97855678
## 23 (88.9,89.7] 225 0.0419541302 4.19541302
## 24 (89.7,90.6] 201 0.0374790229 3.74790229
## 25 (90.6,91.4] 162 0.0302069737 3.02069737
## 26 (91.4,92.3] 157 0.0292746597 2.92746597
## 27 (92.3,93.2] 109 0.0203244453 2.03244453
## 28 (93.2,94] 83 0.0154764125 1.54764125
## 29 (94,94.9] 60 0.0111877680 1.11877680
## 30 (94.9,95.7] 40 0.0074585120 0.74585120
## 31 (95.7,96.6] 17 0.0031698676 0.31698676
## 32 (96.6,97.5] 9 0.0016781652 0.16781652
## 33 (97.5,98.3] 5 0.0009323140 0.09323140
## 34 (98.3,99.2] 5 0.0009323140 0.09323140
Haciendo un pastel de esta tabla de intervalos
Primero las etiquetas que son las clases y sus rangos
Luego las frecuencias en el pastel
# install.packages("plotrix")
library(plotrix)
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(tabla.intervalos$Freq, " Q de ", tabla.intervalos$Var1)
# recordar que n.prom.mayor.cero
# es la cantidad de alumnos con promedio mayor que cero
pie3D(tabla.intervalos$Freq, labels = etiquetas, main = paste("Frecuencia de clases. ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
# En porcentaje %
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(round(tabla.intervalos$Freq.Porc,2), " % de ", tabla.intervalos$Var1)
pie3D(round(tabla.intervalos$Freq.Porc,2), labels = etiquetas, main = paste("Frecuencia de clases. % ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
Determinando las frecuencias por clases (cortes). Los intervalos de clases. FD (Freedman-Diaconis)
# 2 * IQ * n elevada (1/3)
# IQ Rango intercuartílico
clases <- nclass.FD(datos$promedio[which(datos$promedio > 0)])
clases
## [1] 41
tabla.intervalos <- transform(table(cut(datos$promedio[which(datos$promedio > 0 )], breaks = clases)))
tabla.intervalos # es un data.frame
## Var1 Freq
## 1 (70,70.7] 3
## 2 (70.7,71.4] 0
## 3 (71.4,72.1] 2
## 4 (72.1,72.8] 1
## 5 (72.8,73.6] 4
## 6 (73.6,74.3] 1
## 7 (74.3,75] 8
## 8 (75,75.7] 12
## 9 (75.7,76.4] 21
## 10 (76.4,77.1] 31
## 11 (77.1,77.8] 79
## 12 (77.8,78.5] 124
## 13 (78.5,79.2] 173
## 14 (79.2,80] 203
## 15 (80,80.7] 257
## 16 (80.7,81.4] 283
## 17 (81.4,82.1] 323
## 18 (82.1,82.8] 352
## 19 (82.8,83.5] 324
## 20 (83.5,84.2] 337
## 21 (84.2,84.9] 351
## 22 (84.9,85.7] 284
## 23 (85.7,86.4] 299
## 24 (86.4,87.1] 258
## 25 (87.1,87.8] 213
## 26 (87.8,88.5] 237
## 27 (88.5,89.2] 201
## 28 (89.2,89.9] 186
## 29 (89.9,90.6] 159
## 30 (90.6,91.3] 140
## 31 (91.3,92.1] 129
## 32 (92.1,92.8] 99
## 33 (92.8,93.5] 89
## 34 (93.5,94.2] 60
## 35 (94.2,94.9] 47
## 36 (94.9,95.6] 32
## 37 (95.6,96.3] 19
## 38 (96.3,97] 6
## 39 (97,97.7] 9
## 40 (97.7,98.5] 3
## 41 (98.5,99.2] 4
# Podemos agregar columnas al Data.Frame. Frecuencia Relativa y Frecuencia Porcentual
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Rel' = tabla.intervalos$Freq / n.prom.mayor.cero)
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Porc' = tabla.intervalos$Freq.Rel * 100)
tabla.intervalos
## Var1 Freq Freq.Rel Freq.Porc
## 1 (70,70.7] 3 0.0005593884 0.05593884
## 2 (70.7,71.4] 0 0.0000000000 0.00000000
## 3 (71.4,72.1] 2 0.0003729256 0.03729256
## 4 (72.1,72.8] 1 0.0001864628 0.01864628
## 5 (72.8,73.6] 4 0.0007458512 0.07458512
## 6 (73.6,74.3] 1 0.0001864628 0.01864628
## 7 (74.3,75] 8 0.0014917024 0.14917024
## 8 (75,75.7] 12 0.0022375536 0.22375536
## 9 (75.7,76.4] 21 0.0039157188 0.39157188
## 10 (76.4,77.1] 31 0.0057803468 0.57803468
## 11 (77.1,77.8] 79 0.0147305613 1.47305613
## 12 (77.8,78.5] 124 0.0231213873 2.31213873
## 13 (78.5,79.2] 173 0.0322580645 3.22580645
## 14 (79.2,80] 203 0.0378519485 3.78519485
## 15 (80,80.7] 257 0.0479209398 4.79209398
## 16 (80.7,81.4] 283 0.0527689726 5.27689726
## 17 (81.4,82.1] 323 0.0602274846 6.02274846
## 18 (82.1,82.8] 352 0.0656349058 6.56349058
## 19 (82.8,83.5] 324 0.0604139474 6.04139474
## 20 (83.5,84.2] 337 0.0628379638 6.28379638
## 21 (84.2,84.9] 351 0.0654484430 6.54484430
## 22 (84.9,85.7] 284 0.0529554354 5.29554354
## 23 (85.7,86.4] 299 0.0557523774 5.57523774
## 24 (86.4,87.1] 258 0.0481074026 4.81074026
## 25 (87.1,87.8] 213 0.0397165765 3.97165765
## 26 (87.8,88.5] 237 0.0441916838 4.41916838
## 27 (88.5,89.2] 201 0.0374790229 3.74790229
## 28 (89.2,89.9] 186 0.0346820809 3.46820809
## 29 (89.9,90.6] 159 0.0296475853 2.96475853
## 30 (90.6,91.3] 140 0.0261047921 2.61047921
## 31 (91.3,92.1] 129 0.0240537013 2.40537013
## 32 (92.1,92.8] 99 0.0184598173 1.84598173
## 33 (92.8,93.5] 89 0.0165951893 1.65951893
## 34 (93.5,94.2] 60 0.0111877680 1.11877680
## 35 (94.2,94.9] 47 0.0087637516 0.87637516
## 36 (94.9,95.6] 32 0.0059668096 0.59668096
## 37 (95.6,96.3] 19 0.0035427932 0.35427932
## 38 (96.3,97] 6 0.0011187768 0.11187768
## 39 (97,97.7] 9 0.0016781652 0.16781652
## 40 (97.7,98.5] 3 0.0005593884 0.05593884
## 41 (98.5,99.2] 4 0.0007458512 0.07458512
Haciendo un pastel de esta tabla de intervalos
Primero las etiquetas que son las clases y sus rangos
Luego las frecuencias en el pastel
Aquí ya no hacemos el pastel porque salen 41 clases
# install.packages("plotrix")
library(plotrix)
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(tabla.intervalos$Freq, " Q de ", tabla.intervalos$Var1)
# recordar que n.prom.mayor.cero
# es la cantidad de alumnos con promedio mayor que cero
# pie3D(tabla.intervalos$Freq, labels = etiquetas, main = paste("Frecuencia de clases. ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.3)
# En porcentaje %
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(round(tabla.intervalos$Freq.Porc,2), " % de ", tabla.intervalos$Var1)
#pie3D(round(tabla.intervalos$Freq.Porc,2), labels = etiquetas, main = paste("Frecuencia de clases. % ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
Determinando las frecuencias por clases (cortes).
Haciendio arbitrariamente 1o cortes
clases <- 10
tabla.intervalos <- transform(table(cut(datos$promedio[which(datos$promedio > 0 )], breaks = clases)))
tabla.intervalos # es un data.frame
## Var1 Freq
## 1 (70,72.9] 6
## 2 (72.9,75.8] 30
## 3 (75.8,78.8] 298
## 4 (78.8,81.7] 1003
## 5 (81.7,84.6] 1377
## 6 (84.6,87.5] 1168
## 7 (87.5,90.4] 792
## 8 (90.4,93.3] 496
## 9 (93.3,96.3] 170
## 10 (96.3,99.2] 23
# Podemos agregar columnas al Data.Frame. Frecuencia Relativa y Frecuencia Porcentual
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Rel' = tabla.intervalos$Freq / n.prom.mayor.cero)
tabla.intervalos <- data.frame(tabla.intervalos, 'Freq.Porc' = tabla.intervalos$Freq.Rel * 100)
tabla.intervalos
## Var1 Freq Freq.Rel Freq.Porc
## 1 (70,72.9] 6 0.001118777 0.1118777
## 2 (72.9,75.8] 30 0.005593884 0.5593884
## 3 (75.8,78.8] 298 0.055565915 5.5565915
## 4 (78.8,81.7] 1003 0.187022189 18.7022189
## 5 (81.7,84.6] 1377 0.256759277 25.6759277
## 6 (84.6,87.5] 1168 0.217788551 21.7788551
## 7 (87.5,90.4] 792 0.147678538 14.7678538
## 8 (90.4,93.3] 496 0.092485549 9.2485549
## 9 (93.3,96.3] 170 0.031698676 3.1698676
## 10 (96.3,99.2] 23 0.004288644 0.4288644
Haciendo un pastel de esta tabla de intervalos
Primero las etiquetas que son las clases y sus rangos
Luego las frecuencias en el pastel
10 CORTES
# install.packages("plotrix")
library(plotrix)
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(tabla.intervalos$Freq, " Q de ", tabla.intervalos$Var1)
# recordar que n.prom.mayor.cero
# es la cantidad de alumnos con promedio mayor que cero
pie3D(tabla.intervalos$Freq, labels = etiquetas, main = paste("Frecuencia de clases. ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
# En porcentaje %
# paste significa concatenar, unir cadenas de caracteres
etiquetas <- paste(round(tabla.intervalos$Freq.Porc,2), " % de ", tabla.intervalos$Var1)
pie3D(round(tabla.intervalos$Freq.Porc,2), labels = etiquetas, main = paste("Frecuencia de clases. % ", n.prom.mayor.cero, " Observaciones"), labelcex = 0.5)
