Sample Mean

The sample mean is the arithmetic average of a set of observations: their sum divided by their number. It is written $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$, where $x_i$ are the observations and $n$ is the sample size. Five monthly returns of 2, -1, 3, 0 and 1 percent sum to 5, giving a sample mean of 1 percent. The sample mean is the standard estimate of the population mean, the true average that would be found if every possible observation could be measured. The general concept is covered under mean.

A sample mean varies from one sample to the next. Its uncertainty is measured by the standard error, the sample standard deviation divided by the square root of $n$. In trading research this matters because average returns are small relative to their variability. A backtest showing a positive mean return is weak evidence unless the mean is large compared with its standard error, which is what a t-statistic measures.