Elementary Statistics: Picturing the World (6th Edition)

Published by Pearson
ISBN 10: 0-32191-121-0
ISBN 13: 978-0-32191-121-6

Chapter 2 - Descriptive Statistics - Section 2.4 Measures of Variation - Exercises: 9


The Empirical Rule is also known as the 68-95-99.7 rule. It says that, for data with a (symmetric) bell-shaped distribution, the standard deviation has the following characteristics. 1. About 68% of the data lie within one standard deviation of the mean. 2. About 95% of the data lie within two standard deviations of the mean. 3. About 99.7% of the data lie within three standard deviations of the mean. Chebychev's Theorem says that: The portion of any data set lying within k standard deviations of the mean is at least $ 1- \frac{1}{k^{2}} $

Work Step by Step

The Empirical Rule applies only to (symmetric) bell-shaped distributions. What if the distribution is not bell-shaped, or what if the shape of the distribution is not known? The Chebychev theorem gives an inequality statement that applies to all distributions.
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