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What is the empirical rule and how does it differ from Chebyshev's inequality?
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.