Understanding Standard Deviation and Variance

While mean and median tell us about the center of a dataset, standard deviation and variance tell us about the spread. Variability indicates how tightly clustered or widely dispersed the data points are.

Variance is a mathematical expectation of the average squared deviations from the mean. Because the differences are squared, variance gives heavier weight to outliers. The units of variance are squared, which can make it difficult to intuitively understand.

Standard deviation is simply the square root of the variance. This converts the unit of measurement back to the original unit. For example, if you are measuring heights in inches, the variance will be in square inches, but the standard deviation will be in inches. It is much easier to interpret.

For normally distributed data, the empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.