In this example, A is a data set where the values are much closer to the mean. But in B, all the data points are far away from the mean in both directions. The difference between the mean absolute deviation and the standard deviation is negligible for data set A. But the difference between the mean absolute deviation and the standard deviation for set B is much higher. The great variability of data points in the data set has caused a significantly higher standard deviation. When the number of data points increases, the difference between MAD and standard deviation will diverge.

In Gaussian distributions, 68.2% of the data points will lie within one standard deviation on both sides of the mean. More than 95% of the data points will lie within two standard deviations on both sides of the mean. Nearly all (99.7%) of the data points will lie within three standard deviations on both sides of the mean.