Question

What is the difference between Empirical Rule and Chebyshev's inequality in determining what fraction of data you expect to see in a given range?

Answer 1

The Empirical Rule and z-scores define what is expected vs. what is unusual for normally distributed data. Chebyshev's Theorem helps with non-normal and unknown distributions.

Given the mean and standard deviation of a data set, what fraction of the data to you expect to see within a range?
 

\begin{array}{|l|l|l|}
\hline & \text { Empirical Rule } & \text { Chebyshev } \\
\hline \text { Data } & \text { Normal } & \text { Unknown } \\
\hline \text { Z-score range } & \text { Precisely } & \text { At Least } \\
\hline+/-1 & 68.26 \% & 0 \% \\
\hline+/-2 & 95.44 \% & 75 \% \\
\hline+/-3 & 99.74 \% & 89 \% \\
\hline+/-4 & 99.99 \% & 94 \% \\
\hline
\end{array}