## Elementary Statistics: Picturing the World (6th Edition)

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 $1- \frac{1}{k^{2}}$