Chebyshev's Theorem enables us to state that a **proportion** of data values **must** be within
a specified number of standard deviation of the mean. The advantage of this theorem is that the theorem applies to any data set
__regardless__ of the shape of the distribution of the data.

Here is the Chebyshev's rule:

At least $(1- \dfrac{1}{z^2})$ of the data values must be within $z$ standard deviation of the mean where $z$ is any value greater than 1.

For z =2, 3, and 4, these are what the theorem states:

- z = 2,
*at least*75% of the data values must be within 2 standard deviations of the mean. - z = 3,
*at least*89% of the data values must be within 3 standard deviations of the mean. - z = 4,
*at least*94% of the data values must be within 4 standard deviations of the mean.

Unlike Chebyshev's theorem, empirical rule can only be applied to data or observations that are believed to approximate symmetric bell-shaped also known as a normal distribution.

For data having a bell-shaped distribution:

- Approximately 68% of data values will be within one standard deviation of the mean.
- Approximately 95% of data values will be within two standard deviations of the mean.
- Almost all of the data values will be within three standard deviations of the mean.

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