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: 29

Answer

The estimated standard deviation is a bit more than the real standard deviation.

Work Step by Step

Range is the difference of the maximum and minimum of the set: range=2.95-0=2.95 Richter scale. Calculated by calculator, the mean is: 1.184 Richter scale. 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=$\frac{(0.7-1.184)^2+(2.2-1.184)^2+...+(1.39-1.184)^2}{50-1}=0.34 Richter scale.$ The standard deviation is the square root of the variance: standard deviation=$\sqrt{0.34}=0.583 Richter scale$. By The Range Rule of Thumb the standard deviation is one fourth of the range: $\frac{2.95}{4}=0.7375$. This estimated standard deviation is a bit more than the real standard deviation.
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