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Chapter 2: Q. 70 (page 138)

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

Find the value that is one standard deviation below the mean.

Short Answer

Expert verified

The value that is one standard deviation below the mean is-49.55

Step by step solution

01

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.

02

Content Explanation

We have calculated,

Mean as,

x→=∑i=1nxinx⇀=∑i=1n(29+37+38+40+58+67+68+69+76+86+87+95+96+96+99+106+112+127+145+150)20x⇀=84.05

Standard deviation as

s=∑i=1n(xi-x⇀)2n-1s=22636.9519s=34.5

Therefore, to obtain the score that is one standard deviation below the mean, subtract the standard deviation from the mean.

So,Standarddeviation-Mean34.5-84.05=-49.55

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