Normal Distribution

In a normal distribution, the mean, median and mode are all equal and sit at the centre of the bell. The spread is described by the standard deviation.

A useful rule of thumb applies: about 68% of values fall within one standard deviation of the mean, about 95% within two standard deviations and about 99.7% within three. For example, if adult heights in a population are normally distributed with a mean of 170 centimetres and a standard deviation of 10, about 95% of people would be between 150 and 190 centimetres tall.

Many natural measurements roughly follow a normal distribution, and averages of large samples tend towards it even when the underlying data do not. This makes it central to statistics, including confidence intervals and hypothesis tests.

In finance, normal distributions are often used to model investment returns. However, real market returns typically have fatter tails than a normal distribution predicts, meaning extreme gains and losses happen more often than the model suggests. Relying too heavily on the normal distribution can lead investors and risk managers to underestimate the chance of severe market crashes.