# Why we sometimes use mean and sometimes use standard deviation to measure volatility

Both the metrics `average true range` and `historical volatility` measure volatility of a financial instrument's price. Average true range measures volatility on an intraday basis, while historical volatity measures volatility on an interday basis.

Why then for average true range do we compute a mean, whereas for historical volatility we compute a standard deviation?

• `historical volatility, we use standard deviation` Volatility is always standard deviation. Where did you get this information from, very curious ? – DumbCoder Feb 16 '15 at 9:20

• `historical volatility` is a deviation measurement (such as standard deviation) that applies two separate mean computations: the first determines the mean of all the values, and the second determines the mean of the individual differences from the first mean.
• `average true range` is a deviation measurement that applies only one mean computation: a bunch of mean-less deviations are computed and then their overall mean is determined.