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 109: 19


Variance:1017.7 Standard deviation:31.9 Range:79.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{9+23+25+88+12+19+74+77+76+73+78}{11}=50.36$: $\mu=50.36.$ Variance=$\frac{\sum (x-\mu)^2}{n}=\frac{(11-50.36)^2+(3-50.36)^2+...+(2-50.36)^2}{11}=1017.7.$ Standard deviation=$\sqrt{variance}=\sqrt{1017.7}=31.9$ Range=maximum value-minimum value=88-9=79$.
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