Chapter 8.1, Problem 2E

To determine

Tocalculate: The population variance of shoes from the given data.

Answer to Problem 2E

The population variance of the shoes with respect to the number of female student is 202.7658.

Explanation of Solution

Given Information:

Selected female student from their school.

Number of pairs of shoes:

50	26	26	31	57	19	24	22	23	38
13	50	13	34	23	30	49	13	15	51

Formula Used:

The variance formula is ${\sigma }^2=\frac{{\displaystyle \sum _{i=1}^n{\left(x_i-{\overline{x}}_{}\right)}^2}}{n-1}$ .

Calculation:

The data recorded for number of shoes of female student.

50	26	26	31	57	19	24	22	23	38
13	50	13	34	23	30	49	13	15	51

The average number of pairs of shoes 30.35.

Selected female student is 20.

To find the variance of the pairs of shoes, use variance formula.

  $\begin{array}{c}{\sigma }^2=\frac{{\displaystyle \sum _{i=1}^n{\left(x_i-{\overline{x}}_{}\right)}^2}}{n-1}\\ =\frac{{\left(50-30.35\right)}^2+{\left(26-30.35\right)}^2+{\left(26-30.35\right)}^2+\cdots +{\left(13-30.35\right)}^2+{\left(15-30.35\right)}^2+{\left(51-30.35\right)}^2}{20-1}\\ =202.7658\end{array}$

Hence, the population variance of the pairs of shoes with respect to the number of female student is202.7658.