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: 31

Answer

The estimated standard deviation is a little less than the real standard deviation, but very close to it.

Work Step by Step

Range is the difference of the maximum and minimum of the set: range=36-0=36 years. Calculated by calculator, the mean is: 15.03 years. 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{(10−15.03)^2+(29−15.03)^2+...+(23−15.03)^2}{33-1}=$94.5 years. The standard deviation is the square root of the variance: standard deviation=$\sqrt{94.5}=9.72$ minutes. By The Range Rule of Thumb the standard deviation is one fourth of the range:$\frac{36}{4}=9$ years. This estimated standard deviation is a little less than the real standard deviation, but very close to it.

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