## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 3 - Statistics for Describing, Exploring, and Comparing Data - 3-3 Measures of Variation - Basic Skills and Concepts - Page 110: 32

#### Answer

The estimated standard deviation is quite a lot less than the real standard deviation.

#### Work Step by Step

Range is the difference of the maximum and minimum of the set: range=127-85=42. Calculated by calculator, the mean is: 101. The variance is the sum of the differences of each value and the mean on the power of two, divided by the number of values minus 1: variance=$\frac{(96−101)^2+(89−101)^2+...+(124−101)^2}{20-1}=$174.5. The standard deviation is the square root of the variance: standard deviation=$\sqrt{174.5}=13.21$. By The Range Rule of Thumb the standard deviation is one fourth of the range:$\frac{42}{4}=10.5$. This estimated standard deviation is quite a lot less than the real standard deviation.

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