Chapter 8.1, Problem 2E

To determine

To calculate: the standard deviation on the basis of given data

Answer to Problem 2E

  $\sigma =14.24$

Explanation of Solution

Given:

Here are the data

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

Formula used:

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

  $\sigma =\sqrt{\frac{{\left(x-\overline{x}\right)}^2}{n-1}}$

Calculation:

  $\begin{array}{c}\overline{x}=\frac{50+26+26+\mathrm{....}+13+15+51}{20}\\ =\frac{607}{20}\\ =30.35\end{array}$

  $\sigma =\sqrt{\frac{{\left(x-\overline{x}\right)}^2}{n-1}}$

  $\begin{array}{c}{\sigma }^2=\frac{{\left(50-30.35\right)}^2+{\left(26-30.35\right)}^2+{\left(26-30.35\right)}^2+\mathrm{.......}{\left(13-30.35\right)}^2+{\left(15-30.35\right)}^2+{\left(51-30.35\right)}^2}{20-1}\\ =\frac{3852.5502}{19}\\ {\sigma }^2=202.7658\\ \sigma =\sqrt{{\sigma }^2}\\ \sigma =\sqrt{202.7658}\\ =14.24\end{array}$