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: 20


Variance:0.83 Standard deviation:0.91 Range:3.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{4+6⋅3+7⋅2+11⋅12}{5}=1.88$: $\mu=1.88.$ Variance=$\frac{\sum (x-\mu)^2}{n}=\frac{(2-1.88)^2+(1-1.88)^2+...+(2-1.88)^2}{25}=0.83.$ Standard deviation=$\sqrt{variance}=\sqrt{0.83}=0.91$ Range=maximum value-minimum value=4-1=3$.
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