The Empirical rule can be used for bell shaped data ONLY. Chebyshev’s inequality on the other hand can be used on any data set to find the percentile of a given value or data point.
The empirical rule is used to calculate the percent of data within a certain range of standard deviations from the average. It states that that 68% of data falls within the first standard deviation from the mean. 95% fall within two standard deviations, and 99.7% of data falls within 3 standard deviations of the mean. This leaves 00.3% of data to fall outside of 3 deviations of the mean. This is very rare considering any probability outside of 00.5% is considered rare in statistics. The empirical rule can be visualized using this bell curve:
Chebyshev’s inequality on the other hand can be used to find any percentile for a given value in a data set. It is less accurate than the empirical rule, because often the data set is not evenly distributed (bell shaped). I believe I’m correct in saying Chebyshev was a russian statistician back in the early 1900’s.
My statistics teacher told me we did not need to memorize or use chebyshev’s inequality- just to know what it does and how it could be useful. The equation is as follows if you need it:
What exactly that equation means and how to interpret it is beyond my skill set, but I hope what I’ve explained thing sufficient enough to solve your problem.
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