Which statistic is squared to calculate variance?

Variance is a measure of how much the values in a dataset deviate from the mean of that dataset. To calculate variance, you take each data point, subtract the mean, and then square that result. The squaring of the deviations is crucial because it ensures that all the differences are positive, thus preventing values that are above the mean from cancelling out those below the mean.

The standard deviation, which is the square root of variance, is derived from variance, and therefore the statistical operation of squaring is directly applied to the deviations used in the calculation of variance. In contrast, the mean itself is not squared for the purpose of calculating variance; rather, it serves as the central reference point for determining the deviations. Similarly, the median and mode, as measures of central tendency, do not involve squaring in relation to variance calculation.