How is sample variance calculated using deviations from the sample mean?

To calculate the sample variance ($s^2$), you must first determine the mean of your data set.1

The calculation follows these steps:

• Find the deviations: Subtract the sample mean from each individual data value ($x_i$) to find the deviation of each point.1
• Square the deviations: Square each of these individual differences.1
• Sum the squares: Add all of these squared deviations together.1
• Divide: Divide the resulting sum by $n-1$, where $n$ is the total number of items in the sample.1

Using $n-1$ (often called Bessel's correction) instead of $n$ provides an unbiased estimate of the population variance from a sample. This measure of variability is fundamental in statistics because it accounts for all data points in a set, unlike simpler measures like the range.1