Moyenne

Moyenne is a statistical term used to denote a measure of central tendency. In French-language contexts, moyenne can refer to several related quantities, most commonly the arithmetic mean, but also geometric and harmonic means, as well as weighted versions. It serves to summarize a data set by a single representative value.

Arithmetic mean: defined as the sum of values divided by the number of values. Formula: x̄ = (x1 + x2 + ... + xn)/n. Example: for 2, 4, 6 the moyenne is 4. Characteristics: sensitive to outliers; used widely in everyday statistics.

Geometric mean: defined for positive numbers as the nth root of the product. Formula: (x1 x2 ... xn)^(1/n). Example: for 2 and 8 it's 4. Used for multiplicative processes and growth rates, especially in finance and biology.

Harmonic mean: defined as n divided by the sum of reciprocals. Formula: n / (1/x1 + 1/x2 + ... + 1/xn). Example: 1, 2, 4 gives 1.714. Used for averaging rates and when the quantities are defined as per-unit quantities.

Weighted mean: if values have weights w_i, the weighted mean is sum(w_i x_i) / sum(w_i). Useful when data points contribute unequally to the average.

Related measures: median and mode. The moyenne and these other measures describe data differently and may be preferred depending on data distribution and purpose.