Average most often refers to the arithmetic mean, but more generally to measures of central tendency that use most, or all, of the data values. Examples include trimmed mean, Winsorized mean, harmonic mean and geometric mean.

If the values of the variable are $X_i$ and there are $n$ values then:

Arithmetic mean: $\bar{x} = \frac{\sum_{i = 1}^{n}X_i}{n}$

Geometric mean: $g = (\prod_{i = 1}^n x_i)^{\frac{1}{n}}$

Harmonic mean: $\frac{1}{H} = \frac{1}{n}\sum_{i = 1}^n \frac{1}{x_i}$

Trimmed mean: $\sigma_{\alpha}=\frac{1}{n-2k}\sum_{i = k+1}^{n-k}x_{(i)}$

where $\alpha$ is the degree of trimming, $k$ is the smallest integer less than or equal to $\alpha n$ and $x_{(i)}$ are ordered values of x.

Source: Dictionary of Statistics by Brian S. Everitt

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