Chapter 1.3, Problem 100E

To determine

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

Answer to Problem 100E

Standard deviation = 1.67

Explanation of Solution

Given:

6

7

7

8

10

10

Formula used:

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

Calculation:

X	${\left(x_i-\overline{x}\right)}^2$
6	4
7	1
7	1
8	0
10	4
10	4
48	14

  $\begin{array}{c}\text{Standard Deviation = }\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n-1}}\\ =\sqrt{\frac{14}{5}}\\ =1.67\end{array}$

The values of the given dataset are scattered from the mean by 1.67 units.