Caso mediciones de personas, estaturas, pesos, generos y otros

datos= read.table("https://raw.githubusercontent.com/rpizarrog/probabilidad-y-estad-stica/master/datos/body.dat.txt", quote="\"", comment.char="")
datos = as.data.frame(datos)
colnames(datos)[23:25] = c("peso", "estatura", "sexo")
datos= select(datos, peso, estatura, sexo)
kable(head(datos))

peso	estatura	sexo
65.6	174.0	1
71.8	175.3	1
80.7	193.5	1
72.6	186.5	1
78.8	187.2	1
74.8	181.5	1

datos$sexo = as.factor(datos$sexo)

summary(datos)

##       peso           estatura     sexo   
##  Min.   : 42.00   Min.   :147.2   0:260  
##  1st Qu.: 58.40   1st Qu.:163.8   1:247  
##  Median : 68.20   Median :170.3          
##  Mean   : 69.15   Mean   :171.1          
##  3rd Qu.: 78.85   3rd Qu.:177.8          
##  Max.   :116.40   Max.   :198.1

ggplot(datos, aes(sexo, peso)) +
  geom_boxplot(colour = c("deeppink", "dodgerblue4"))

ggplot(datos, aes(sexo, estatura)) +
  geom_boxplot(colour = c("deeppink", "dodgerblue4"))

h= filter(datos, sexo==1)
m= filter(datos, sexo==0)

Hombres Media, mínimo, máximo, mediana y cuantiles

summary(h)

##       peso           estatura     sexo   
##  Min.   : 53.90   Min.   :157.2   0:  0  
##  1st Qu.: 70.95   1st Qu.:172.9   1:247  
##  Median : 77.30   Median :177.8          
##  Mean   : 78.14   Mean   :177.7          
##  3rd Qu.: 85.50   3rd Qu.:182.7          
##  Max.   :116.40   Max.   :198.1

Desviaciones estándar *Peso

mhp=mean(h$peso)
shp=sd(h$peso)
shp

## [1] 10.51289

*Estatura

mhe=mean(h$estatura)
she=sd(h$estatura)
she

## [1] 7.183629

Mujeres Media, mínimo, máximo, mediana y cuantiles

summary(m)

##       peso          estatura     sexo   
##  Min.   : 42.0   Min.   :147.2   0:260  
##  1st Qu.: 54.5   1st Qu.:160.0   1:  0  
##  Median : 59.0   Median :164.5          
##  Mean   : 60.6   Mean   :164.9          
##  3rd Qu.: 65.6   3rd Qu.:169.5          
##  Max.   :105.2   Max.   :182.9

Desviaciones estándar *Peso

mmp=mean(m$peso)
smp=sd(m$peso)
smp

## [1] 9.615699

*Estatura

mme=mean(m$estatura)
smh=sd(m$estatura)
smh

## [1] 6.544602

Cálculo de probabilidades 1. Probabilidad de que un hombre pese más de 60 kilos

plotDist("norm", mean = mhp, sd = shp, groups = x > 60, type = "h", xlab = "Peso Hombres", ylab = "Densidad" )

1-pnorm(q = 60, mean = mhp, sd = shp, )

## [1] 0.9578202

2. Probabilidad de que un hombre pese entre 70 y 80 kg

plotDist("norm", mean = mhp, sd = shp, groups = x > 70 & x<80, type = "h", xlab = "Peso Hombres", ylab = "Densidad" )

pnorm(q = 80, mean = mhp, sd = shp, )-pnorm(q = 70, mean = mhp, sd = shp, )

## [1] 0.3507943

3. Probabilidad de que un hombre pese menos de 75kg

plotDist("norm", mean = mhp, sd = shp, groups =x<75, type = "h", xlab = "Peso Hombres", ylab = "Densidad" )

pnorm(q = 75, mean = mhp, sd = shp, )

## [1] 0.3824272

4. Probabilidad de que una mujer pese más de 55kg

plotDist("norm", mean = mmp, sd = smp, groups = x > 55, type = "h", xlab = "Peso Mujeres", ylab = "Densidad" )

1-pnorm(q = 55, mean = mmp, sd = smp, )

## [1] 0.7198584

5. Probabilidad de que una mujer pese entre 50 y 60 kg

plotDist("norm", mean = mmp, sd = smp, groups = x > 50 & x<60, type = "h", xlab = "Peso Mujeres", ylab = "Densidad" )

pnorm(q = 60, mean = mmp, sd = smp, )-pnorm(q = 50, mean = mmp, sd = smp, )

## [1] 0.339964

6. Probabilidad de que una mujer pese menos de 45kg

plotDist("norm", mean = mmp, sd = smp, groups =  x<45, type = "h", xlab = "Peso Mujeres", ylab = "Densidad" )

pnorm(q = 45, mean = mmp, sd = smp, )

## [1] 0.05236025

7. Probabilidad de que un hombre mida más de 165cm

plotDist("norm", mean = mhe, sd = she, groups = x > 165, type = "h", xlab = "Estatura Hombres", ylab = "Densidad" )

1-pnorm(q = 165, mean = mhe, sd = she, )

## [1] 0.9619867

8. Probabilidad de que un hombre mida entre 175 y 185

plotDist("norm", mean = mhe, sd = she, groups = x > 175 & x<185, type = "h", xlab = "Estatura Hombres", ylab = "Densidad" )

pnorm(q = 185, mean = mhe, sd = she, )-pnorm(q = 175, mean = mhe, sd = she, )

## [1] 0.4925565

9. Probabilidad de que un hombre mida menos de 170cm

plotDist("norm", mean = mhe, sd = she, groups =x<170, type = "h", xlab = "Estatura Hombres", ylab = "Densidad" )

pnorm(q = 170, mean = mhe, sd = she, )

## [1] 0.1404736

10. Probabilidad de que una mujer mida más de 155cm

plotDist("norm", mean = mme, sd = smh, groups = x > 155, type = "h", xlab = "Estatura Mujeres", ylab = "Densidad" )

1-pnorm(q = 155, mean = mme, sd = smh, )

## [1] 0.9342823

11. Probabilidad de que una mujer mida entre 165 y 170

plotDist("norm", mean = mme, sd = smh, groups = x > 165 & x<170, type = "h", xlab = "Peso Mujeres", ylab = "Densidad" )

pnorm(q = 170, mean = mme, sd = smh, )-pnorm(q = 165, mean = mme, sd = smh, )

## [1] 0.2755498

12. Probabilidad de que una mujer mida menos de 155

plotDist("norm", mean = mme, sd = smh, groups =  x<155, type = "h", xlab = "Estatura Mujeres", ylab = "Densidad" )

pnorm(q = 155, mean = mme, sd = smh, )

## [1] 0.06571769