What is Chebyshev's inequality?
Chebyshev’s inequality says that at least
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.