Normal Distribution & The Empirical Rule

A normal distribution looks a little bit like the below. It’s where the mean, median and mode are on top of one another.

Remember in a previous article, we discussed Chebyshev’s theorem, which gave us a guideline for what percentage of datapoints fell between two intervals? Well, the empirical rule is the same, but better. It gives us a much more accurate approximation of the percentage of data that falls between certain intervals – but, unlike Chebyshev’s theorem, only works for normally distributed data.

Here’s how they compare:

If we look at the empirical rule, it states the approximate amount of data that will fall between our sigma intervals. The below chart shows this graphically.

So, we simply take the mean and +/- sigma to define our upper and lower boundaries.