Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 3 - Data Description - 3-2 Measures of Variation - Exercises 3-2 - Page 146: 39



Work Step by Step

Chebyshev’s theorem The proportion of values from a data set that will fall within k standard deviations of the mean will be at least $1−1/k^2$, where k is a number greater than 1 (k is not necessarily an integer). 39. Farm Sizes The average farm in the United States in 2004 contained 443 acres. The standard deviation is 42 acres. Use Chebyshev’s theorem to find the minimum percentage of data values that will fall in the range of 338–548 acres. $42k=548-443$ we have $k=2.5$ and $1-1/2.5^2=0.84$
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