Question

The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles. $29;37;38;40;58;67;68;69;76;86;87;95;96;96;99;106;112;127;145;150$Use a graphing calculator or computer to find the standard deviation and round to the nearest tenth.

Short answer

$S\tan darddeviation=34.5$

Step-by-step solution

Content Introduction

A "typical" divergence from the mean is indicated by the standard deviation. Because it returns to the data set's original units of measure, it's a common measure of variability.

Content Explanation

We are given set of values:

$29;37;38;40;58;67;68;69;76;86;87;95;96;96;99;106;112;127;145;150$

The total number of values are $20$

Let us first find out mean.

$Mean=\overrightarrow{x}=\frac{\sum _{i=1}^n{x}_i}{n}$

here, $n=20$

$$\begin{gathered} \overrightarrow{x}=\frac{\sum _{i=1}^n{x}_i}{n} \\ \stackrel{\rightharpoonup }{x}=\frac{\sum _{i=1}^n(29+37+38+40+58+67+68+69+76+86+87+95+96+96+99+106+112+127+145+150)}{20} \\ \stackrel{\rightharpoonup }{x}=84.05 \end{gathered}$$

Standard deviation is

$$\begin{gathered} s=\sqrt{\frac{\sum _{i=1}^n{(x_i-\stackrel{\rightharpoonup }{x})}^2}{n-1}} \\ s=\sqrt{\frac{22636.95}{19}} \\ s=34.5 \end{gathered}$$