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.
