As stated before, the standard deviation is a measure of the spread of a distribution. Here are several normal curves with the same center, but different population standard deviations:
As you can see, as the spread of the distribution increases, so does σ. Therefore, the area of the curve lying within a certain number of standard deviations from the mean is fixed, over all normal distributions. Specifically:
- 68% of the area of the curve is within the range of μ ± 1σ
- 95% of the area of the curve is within the range of μ ± 2σ
- 99% of the area of the curve is within the range of μ ± 3σ
Commit these numbers to memory: 68-95-99!
