Chapter 10.3, Problem 23PFA

To determine

To calculate the standard deviation

Answer to Problem 23PFA

Standard deviation is 4.6

Explanation of Solution

Given information:

Data set is,

0, 8, 14, 1, 12, 6, 6, 10

Formula Used:

Standard deviation is,

  $SD=\sqrt{\frac{{\displaystyle \sum }{(x-\overline{x})}^2}{n}}$

Where, SD= standard deviation,

x = value

The Range is the difference between the lowest and highest values.

For mean,

  $\overline{x}=\frac{0+8+14+1+12+6+6+10}{8}$

So,

  $\overline{x}=\frac{57}{8}$

On solving,

  $\overline{x}=7.13$

Hence, mean is 7.13.

For standard deviation substituting the values,

  $SD=\sqrt{\frac{\begin{array}{}$ {(0-7.13)}^2+{(8-7.13)}^2+{(14-7.13)}^2+{(1-7.13)}^2+{(12-7.13)}^2+{(6-7.13)}^2+{(6-7.13)}^2$$ +{(10-7.13)}^2$\end{array}}{8}}$

So,

  $SD=\sqrt{\frac{{(-7.13)}^2+{(0.87)}^2+{(6.87)}^2+{(-6.13)}^2+{(4.87)}^2+{(-1.13)}^2+{(-1.13)}^2+{(2.87)}^2}{8}}$

On solving,

  $SD=\sqrt{\frac{170.88}{8}}$

So,

  $SD=\sqrt{21.36}$

On solving,

  $SD=4.63$

Hence, standard deviation is 4.6