Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 3 - Statistics for Describing, Exploring, and Comparing Data - 3-3 Measures of Variation - Basic Skills and Concepts - Page 109: 26


Range:37 minutes, variance:85.5 minutes, standard deviation: 9.247 minutes.

Work Step by Step

Range is the difference of the maximum and minimum of the set: range=49-12=37 minutes. Calculated by calculator, the mean is: 20.98 minutes. The variance is the sum of the differences of each value and the mean on the power of two, divided by the number of values minus 1: variance=$\frac{(30-20.98)^2+(19-20.98)^2+...+(30-20.98)^2}{50-1}=85.5$ minutes. The standard deviation is the square root of the variance: standard deviation=$\sqrt{85.5}=9.247$ minutes.
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