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 standard deviation $\sigma$.

Short answer

The standard deviation is $\sigma =14.24$

Step-by-step solution

Given Information

We are given the data of twenty students recording number of pair of shoes.

Concept Used

Formula to used $\overline{x}=\frac{\sum x}{n}$

$\sigma =\sqrt{\frac{(x-\overline{x}{)}^2}{n-1}}$

Simplification

Mean is calculated as $\overline{x}=\frac{50+26+26+\dots .+13+15+51}{20}$

$=\frac{607}{20}$

$=30.35$

Also

$\sigma =\sqrt{\frac{(x-\overline{x}{)}^2}{n-1}}$

${\mathit{\sigma }}^2=\frac{(50-30.35{)}^2+(26-30.35{)}^2+(26-30.35{)}^2+\dots \dots ..(13-30.35{)}^2+(15-30.35{)}^2+(51-30.35{)}^2}{20-1}$

$=\frac{3852.5502}{19}$

${\sigma }^2=202.7658$

$\sigma =\sqrt{{\sigma }^2}$

$\sigma =\sqrt{202.7658}$

$\sigma =14.24$