# Standard deviation

Standard deviation (SD) is still the most widely used measure of dispersion, or in financial markets, risk. That all sounds a bit technical but it’s actually pretty straightforward to understand.

It is based on the idea that any population is “normally distributed” – in other words, whether it contains the height of every UK adult female, or the annual return from the FTSE 100 over 100 years, most members of a given group will be bunched around the arithmetic average for the whole group.

For the heights example, this would be the sum of every woman’s height divided by the number of women in the UK. So a randomly chosen woman in the UK will on average be close to say 5’5″ – with only a few people significantly above or below that “mean” height (so-called “outliers”).

SD quantifies the average dispersion of, say, heights or equity returns, above or below the mean figure. In other words, it’s a measure of how widely the data varies from the mean. Given a normal distribution, about two-thirds of all the data points in a set should lie with one SD of the mean, and almost 100% should lie within three SD.

The higher the SD, the wider the spread of the data – or the greater the risk that a randomly chosen woman from your data set is nowhere near the average of 5’5″, or that the return from equities next year is way above or below the past 100-year average.