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 110: 30


The estimated standard deviation is slightly more than the real standard deviation, but very close to it.

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}{48-1}=$85.5 minutes. The standard deviation is the square root of the variance: standard deviation=$\sqrt{85.5}=9.247$ minutes. By The Range Rule of Thumb the standard deviation is one fourth of the range:$\frac{37}{4}=9.25$ minutes. This estimated standard deviation is a littlebit more than the real standard deviation, but very close to it.
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