# What is Chebyshev's inequality?

##### 1 Answer

Jan 21, 2016

Chebyshev’s inequality says that at least

#### Explanation:

Let play with a few value of K:

#K = 2# we have#1-1/K^2 = 1 - 1/4 = 3/4 = 75%# . So Chebyshev’s would tell us that 75% of the data values of**any**distribution must be within**two**standard deviations of the mean.#K = 3# we have#1 – 1/K^2 = 1 - 1/9 = 8/9 = 89%# . This time we have 89% of the data values within**three**standard deviations of the mean.#K = 4# we have#1 – 1/K^2 = 1 - 1/16 = 15/16 = 93.75%# . Now we have 93.75% of the data within**four**standard deviations of the mean.

This is consistent to saying that in Normal distribution 68% of the data is **one** standard deviation from the mean, 95% is **two** standard deviations from the mean, and approximately 99% is within **three** standard deviations from the mean. The difference is Chebyshev's theorem extends this principle to any distribution.