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: 9

Answer

Variance:$210.86 \ (m\$)^2$. Standard deviation:$14.52 \ m\$$ Range:$54 \ m\$$.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{58+22+27+29+21+10+10+8+7+9+11+9+4+4}{14}=16.36$: $\mu=16.36 \ m\$.$ Variance=$\frac{\sum (x-\mu)^2}{n}=\frac{(58-16.36)^2+(22-16.36)^2+...+(4-16.36)^2}{14}=210.86 \ (m\$)^2.$ Standard deviation=$\sqrt{variance}=\sqrt{210.86 \ (m\$)^2}=14.52 \ m\$$ Range=maximum value-minimum value=$58 \ m\$-4 \ m\$=54 \ m\$$.
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