Standard Deviation

Standard deviation is a number that describes how spread out a set of values is around their average. In trading, it's most often used to measure how much a price (or a return, meaning the percentage change in price over some period) bounces around its own average value. A small standard deviation means prices have been sticking close to the average — calmer, tighter action. A large standard deviation means prices have been swinging widely away from the average — choppier, more volatile action.

The way it's calculated: take a series of prices or returns, find their average, measure how far each one sits from that average, square those distances (so negative and positive differences don't cancel out), average the squared distances, then take the square root of that result to bring the units back to something comparable to the original price. You rarely need to do this by hand — charting platforms and spreadsheets compute it instantly — but knowing the shape of the calculation helps explain why standard deviation reacts the way it does: a few sharp outlier moves can push it up quickly, and it settles back down as calm trading days accumulate in the sample.

The nuance that trips people up is that standard deviation measures dispersion, not direction. A stock that has moved up steadily every day and a stock that has whipped up and down and ended flat can, in theory, produce similar standard deviation readings if the size of the daily moves is similar — the calculation doesn't know or care which way price went, only how far it strayed from its average. It's a measure of uncertainty or variability, not a signal of bullish or bearish intent. It's also backward-looking by construction: it tells you how spread out past prices were, not what will happen next, though traders use it as a working estimate of how much a price might continue to move.

Standard deviation also underlies many other tools you'll encounter, most directly Bollinger Bands, which are plotted a chosen number of standard deviations above and below a moving average to visualize when price is stretched relative to its recent range.