How is variance calculated for a data set?

Variance measures the dispersion of a set of values around their mean. To calculate variance, you first determine the mean (average) of the data set, then subtract the mean from each individual value to find the deviation of each value from the mean. These deviations are squared to eliminate negative values, ensuring that positive and negative differences do not cancel each other out. Next, you sum all of these squared deviations and divide by the number of values in the data set to find the average of these squared differences.

Therefore, the correct formulation involves subtracting the mean from each value, squaring those differences to account for their magnitude, and then averaging these squared differences. This process accurately reflects how spread out the data is from the mean, thus providing a true measure of variance.