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.