As stated before, the standard deviation measures the spread of a distribution. Here are several normal curves with the same center but different populated standard deviations:
As the spread of the distribution increases, so does the standard deviation (σ). Therefore, the area of the curve lying within a certain number of standard deviations from the mean (μ) 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!
