Descriptive Statistics: Mean, Median, StdDev for Traders

A chart shows you prices. Statistics tell you what those prices actually mean.

Before any strategy, indicator, or backtest, a trader needs to understand the shape of the data they're trading. Descriptive statistics compress hundreds of bars into a few numbers that describe where price tends to sit and how wildly it swings.

Mean: the center of mass

The arithmetic mean is the average:

Mean (μ) = (Σ xi) ÷ n

In trading, the mean of closing prices over a window is the simplest trend proxy — it's literally what a simple moving average plots. But the mean is fragile. A single gap or one wild candle can drag it far from where most prices actually cluster.

Median: the honest center

The median is the middle value when prices are sorted. Unlike the mean, it ignores magnitude — it only counts position.

Mean pulled above median → positive skew (a few large up-moves)
Mean pulled below median → negative skew (a few large down-moves)

For intraday or skewed instruments, the median is often a more honest "typical price" than the mean. Compare the two: when they disagree sharply, the market has fat tails or recent shocks.

Standard deviation: the noise gauge

Standard deviation measures dispersion around the mean:

σ = sqrt( Σ(xi − μ)² ÷ (n − 1) )

The sample version divides by n − 1 to stay unbiased. In markets, σ is volatility:

High σ → wide ranges, larger stops needed
Low σ → quiet, range-bound behavior

This is the same σ that Bollinger Bands and most volatility stops are built on. Treat it as the unit of risk for any period you're trading.

A worked example

Say 5 daily closes: 100, 101, 102, 103, 120.

Mean = 105.2
Median = 102
σ ≈ 7.7

The mean (105.2) sits well above the median (102) — a red flag for skew. The outlier (120) distorted the mean but barely moved the median. A trader who sized off the mean would underestimate how extreme the last bar was relative to "normal."

How to use them together

Compute mean and median over your trading window
If they diverge, expect skew and use median-based stops
Use σ to set position size and stop distance
Recalculate as the window shifts — these are descriptive, not predictive

Summary

Mean tells you the center. Median tells you the typical price. Standard deviation tells you how loud the market is. Together they form the foundation every other statistical tool — from z-scores to Bollinger Bands — is built on.