Standard Deviation

Standard deviation expresses spread in the same units as the original data, which makes it easier to interpret than variance. A low standard deviation means values tend to be close to the mean; a high one means they are more widely scattered.

For the values 2, 4, 6 and 8, the population variance is 5, so the population standard deviation is about 2.24. In other words, the values typically lie a little over 2 units from their mean of 5.

In finance, standard deviation is the most common measure of volatility. If two funds both average annual returns of 7%, but one has a standard deviation of 5% and the other 15%, the second fund's returns swing much more from year to year, making it riskier in the short term.

When data follow a normal distribution, standard deviation has a useful interpretation: about 68% of values fall within one standard deviation of the mean, and about 95% within two. For a fund averaging 7% with a standard deviation of 15%, returns between −8% and 22% would be expected in roughly two years out of three, if returns were normally distributed. Real market returns often have more extreme outcomes than this simple rule suggests.