Chapter 1.3, Problem 99E

To determine

To calculate the median of the given data and interpret the result.

Answer to Problem 99E

Standard deviation = 2.52

Explanation of Solution

Given:

25

22

20

25

24

24

28

Formula used:

  $\text{Standard Deviation = }\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n-1}}$

Calculation:

X	${\left(x_i-\overline{x}\right)}^2$
25	1
22	4
20	16
25	1
24	0
24	0
28	16
168	38

  $\begin{array}{c}\text{Standard Deviation = }\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n-1}}\\ =\sqrt{\frac{38}{6}}\\ =2.52\end{array}$

The values of the given dataset are scattered from the mean by 2.52 units.