Importance of Chebyshev’s Theorem
Nov 9, 2022
The Empirical Rule, or the 68–95–99.7 rule, can be used only for normal distribution.
But when the distribution does not follow a normal distribution, Chebyshev’s Theorem can be used which is independent of the shape of the distribution.
That is, Chebyshev’s Theorem is used when:
- Data is not normally distributed
- Dataset is heavily skewed
More about normal distribution and skewness can be read here.
Chebyshev’s Theorem states that for any dataset, the percentage of values that are found within distances of k standard deviations from the mean must be at least
Comparison of Chebyshev’s Theorem to Empirical Rule:
For 1st Standard deviation % of value found is at least 0%. Chebyshev’s Theorem always gives approximation.
The minimum and Maximum % with standard deviation with mean is below.
