Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 3 - Statistics for Describing, Exploring, and Comparing Data - 3-3 Measures of Variation - Page 108: 17


Variance:231.4 Standard deviation:15.2 Range:43.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{−15−18−32−21−9−32+11+2}{8}=−14.25$: $\mu=(-14.25).$ Variance=$\frac{\sum (x-\mu)^2}{n}=\frac{((-15)-(-14.25))^2+((-18)-(-14.25))^2+...+(2-(-14.25))^2}{8}=231.4.$ Standard deviation=$\sqrt{variance}=\sqrt{231.4}=15.2$ Range=maximum value-minimum value=$11-(-32)=43$.
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