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: 13


Variance:41.75. Standard deviation:6.46 Range:17.5.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{3+6.5+6+5.5+20.5+7.5+12+20.5+11.5+17.5}{10}=11.05$: $\mu=11.05$ Variance=$\frac{\sum (x-\mu)^2}{n}=\frac{(3-11.05)^2+(6.5-11.05)^2+...+(17.5-11.05)^2}{5}=41.75.$ Standard deviation=$\sqrt{variance}=\sqrt{41.75}=6.46$ Range=maximum value-minimum value=$20.5-3=17.5$.
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