ESTADISTICA DESCRIPTIVA

Estadística Descriptiva
Juan Sebastián Zubiria
Eugenio Andrés Piñerez
Grupo 3°
##########################DISTRIBUCIÓN DE FRECUENCIAS###########################
#Se seleccionaron aleatoriamente en un proceso de desempeño en una empresa de #programación, 100 personas para hallar algún tipo de regularidad en el proceso. #En el cuadro se dan los datos que representan #las notas de la prueba de cada#uno de los programadores:

datos<-c(10, 9, 9, 10, 4, 6, 7, 2, 2, 2, 3, 3,

9, 4, 10, 4, 6, 3, 7, 3, 6, 4, 3, 8, 4,

3, 7, 5, 3, 4, 6, 5, 8, 7, 9, 8, 8, 7,

7, 5, 8, 10, 6, 6, 10, 6, 4, 6, 3, 9, 9,

5, 5, 10, 9, 8, 6, 8, 8, 9, 8, 9, 8, 4,

3, 5, 3, 6, 9, 4, 7, 5, 3, 6, 7, 6, 4,

8, 6, 7,4, 8, 6, 10, 5, 6, 8, 5, 8, 9,

8, 4, 5, 6, 8, 7, 7, 9, 5, 8)

# Los número de datos son :
n=length(datos)
n
## [1] 100
# Ordenamos los datos de menor a mayor:
datos=sort(datos)
datos
#[1] 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4

#[24] 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6

#[47] 6 6 6 6 6 6 6 7 7 7 7 7 7 77 7 7 7 8 8 8 8 8

#[70] 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9

# [93] 9 10 10 10 10 10 10 10
# Valor menor y valor mayor:
R=range(datos)
R
## [1] 2 10

#número de clases
nuclases=nclass.Sturges(datos)
nuclases
## [1] 8

#Longitud de clase
L=(max(datos)-min(datos))/nuclases
L
## [1] 1

#puntos de cortes para las clases
limites = seq(1, 10, by=1)
limites
##[1] 1 2 3 4 5 6 7 8 9 10
#límites establecidos anteriormente
#los límites para las clases
clases= factor(cut(datos, limites))
clases
## [1] (1,2] (1,2] (1,2] (2,3] (2,3] (2,3] (2,3] (2,3] (2,3] (2,3]
## [11] (2,3] (2,3] (2,3] (2,3] (3,4] (3,4] (3,4] (3,4] (3,4] (3,4]
## [21] (3,4] (3,4] (3,4] (3,4] (3,4] (3,4] (4,5] (4,5] (4,5] (4,5]
## [31] (4,5](4,5] (4,5] (4,5] (4,5] (4,5] (4,5] (5,6] (5,6] (5,6]
## [41] (5,6] (5,6] (5,6] (5,6] (5,6] (5,6] (5,6] (5,6] (5,6] (5,6]
## [51] (5,6] (5,6] (5,6] (6,7] (6,7] (6,7] (6,7] (6,7] (6,7] (6,7]
## [61] (6,7] (6,7] (6,7] (6,7] (7,8] (7,8] (7,8] (7,8] (7,8] (7,8]
## [71] (7,8] (7,8] (7,8] (7,8] (7,8] (7,8] (7,8] (7,8] (7,8] (7,8]
## [81] (7,8] (8,9](8,9] (8,9] (8,9] (8,9] (8,9] (8,9] (8,9] (8,9]
## [91] (8,9] (8,9] (8,9] (9,10] (9,10] (9,10] (9,10] (9,10] (9,10] (9,10]
## Levels: (1,2] (2,3] (3,4] (4,5] (5,6] (6,7] (7,8] (8,9] (9,10]


#Las clases con sus respectivas frecuencias
table(clases)
## clases
## (1,2] (2,3] (3,4] (4,5] (5,6] (6,7] (7,8] (8,9] (9,10]
## 3 11 12 11 16 11 17 127

#clases y frecuencias absolutas
frec=as.data.frame(table(clases))
frec
## clases Freq
## 1 (1,2] 3
## 2 (2,3] 11
## 3 (3,4] 12
## 4 (4,5] 11
## 5 (5,6] 16
## 6 (6,7] 11
## 7 (7,8] 17
## 8 (8,9] 12
## 9 (9,10] 7
#Las clases
clases=frec$clases
clases
## [1] (1,2] (2,3] (3,4] (4,5] (5,6] (6,7] (7,8] (8,9] (9,10]
## Levels: (1,2] (2,3] (3,4] (4,5] (5,6] (6,7](7,8] (8,9] (9,10]

#Las frecuencias absolutas:
f=frec$Freq
f
## [1] 3 11 12 11 16 11 17 12 7

#Las frecuencias relativas o porcentual
fr=f/100
fr
## [1] 0.03 0.11 0.12 0.11 0.16 0.11 0.17 0.12 0.07
#la frecuencias acumuladas:
Fa=cumsum(f)
Fa
## [1] 3 14 26 37 53 64 81 93 100
#frecuencias relativas
Far=Fa/100
Far
## [1] 0.03 0.14 0.26 0.37 0.53 0.64 0.81 0.93 1.00
#Marcas de clases,son los puntos medios de cada clase:
x=(seq(1,9,by=1)+seq(2,10,by=1))/2
x
## [1] 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

#distribución de frecuencias correspondiente a la prueba de 100
#programadores, seleccionadas de manera aleatoria, de la producción de una #fábrica en una semana.
data.frame(clases, x ,f,Fa,fr,Far)
## clases x f Fa fr Far
## 1 (1,2] 1.5 3 3 0.03 0.03
## 2 (2,3] 2.5...