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

Answer

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.