Variance (Statistics)

Variance tells you how far, on average, values lie from their mean. A small variance means values are clustered tightly around the mean; a large variance means they are widely spread.

To calculate it, find the mean, subtract it from each value, square each difference, add the squares and divide. For the values 2, 4, 6 and 8, the mean is 5. The differences are −3, −1, 1 and 3, and their squares are 9, 1, 1 and 9, which add up to 20. Dividing by the number of values, 4, gives a population variance of 5. When the data are a sample from a larger population, statisticians usually divide by one less than the number of values, 3, giving a sample variance of about 6.67.

The differences are squared so that positive and negative deviations do not cancel out, and so that larger deviations count more heavily.

In finance, variance is used to measure the risk of investment returns. Because it is in squared units, which are hard to interpret, people usually look at its square root, the standard deviation. Variance is still important in portfolio theory, where the variances of individual assets and their covariances determine a portfolio's overall risk.