Question

Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs of shoes that female students have by estimating the population variance ${\sigma }^2$.

Short answer

The sample variance is $s^2=202.7658$.

Step-by-step solution

Given Information

Data:

Explanation

The mean (or average) is the sum of all values divided by the number of values:

$\overline{x}=\frac{50+26+\dots +15+51}{20}=30.35$

$n$is the number of values in the data set.

$n=20$

The sample variance is the sum of squared deviations from the mean divided by $n-1$:

$s^2=\frac{\sum (x-\overline{x}{)}^2}{n-1}$

$(50-30.35{)}^2+(26-30.35{)}^2+(26-30.35{)}^2+(31-30.35{)}^2+(57-30.35{)}^2$

$+(19-30.35{)}^2+(24-30.35{)}^2+(22-30.35{)}^2+(23-30.35{)}^2+(38-30.35{)}^2$

$+(13-630.35{)}^2+(50-30.35{)}^2+(13-30.35{)}^2+(34-30.35{)}^2+(23-30.35{)}^2$

$\frac{+(30-30.35{)}^2+(49-30.35{)}^2+(13-30.35{)}^2+(15-30.35{)}^2+(51-30.35{)}^2}{20-1}$

$=202.7658$