Chapter 10.2, Problem 41E

To determine

The pairs of shoes having by teenagers is to be calculated.

Answer to Problem 41E

Females and males groups have $30.5$ and $11.6$ pairs of shoes respectively.

Explanation of Solution

Given:

Males	Females
$14$	$50$
$7$	$26$
$6$	$26$
$5$	$31$
$12$	$57$
$37$	$19$
$8$	$24$
$7$	$22$
$10$	$23$
$10$	$38$
$10$	$13$
$11$	$50$
$4$	$13$
$5$	$34$
$22$	$23$
$7$	$30$
$5$	$49$
$10$	$13$
$35$	$15$
$7$	$51$

Concept Used:

The Mean formula:

  $\overline{X}=\frac{{\displaystyle \sum X}}{n}$

Where,

Sum of all data values: ${\displaystyle \sum X}$

Number of data values: $n$

Calculation:

Let’s take given table and find out its sum first:

Males	Females
$14$	$50$
$7$	$26$
$6$	$26$
$5$	$31$
$12$	$57$
$37$	$19$
$8$	$24$
$7$	$22$
$10$	$23$
$10$	$38$
$10$	$13$
$11$	$50$
$4$	$13$
$5$	$34$
$22$	$23$
$7$	$30$
$5$	$49$
$10$	$13$
$35$	$15$
$7$	$51$
${\displaystyle \sum 232}$	${\displaystyle \sum 607}$

Now, the pairs of shoes having by teenagers is calculated by calculating the mean:

  $\begin{array}{l}{\overline{X}}_M=\frac{{\displaystyle \sum 232}}{n}=\frac{232}{20}=11.6\\ {\overline{X}}_F=\frac{{\displaystyle \sum 607}}{n}=\frac{232}{20}=30.5\end{array}$

Conclusion:

Hence, females and males groups have $30.5$ and $11.6$ pairs of shoes respectively.