Standard deviation

A dispersion measure. Each value's distance from the mean is squared, the squares are averaged, and the root of that average is taken. Squaring makes every distance positive so that movements in opposite directions do not cancel, and taking the root returns the answer to the units of the original data, so a standard deviation of closing prices is quoted in the same units the prices are quoted in.

One property of that procedure matters more than the rest. Because the distances are squared before they are averaged, a single large departure contributes far more than several small ones, so the measure is dominated by the extremes of the window rather than by its typical bar. That is what makes it responsive to a change in conditions, and it is also why a quiet stretch containing one violent bar produces a reading that describes neither.

It is the input to several familiar objects. Bollinger Bands are a moving average with a multiple of it added and subtracted; historical volatility is it computed over returns and annualised; and risk measures that compare a result to the variability that produced it use it as the denominator. The reading it produces is a description of the window it was computed over and carries no statement about what the next bar will do.