 Mean (mathematics)

A mathematical mean assigns a representative value to several quantities. A real mean of $x_1,\dots ,x_n$ normally lies between their minimum and maximum and returns $x$ when every input equals $x$. Different means preserve different operations: the arithmetic mean averages sums, while the geometric mean averages positive multiplicative factors.

For $2$ and $8$, the arithmetic mean is $5$ and the geometric mean is $4$. If equal distances are traveled at speeds $2$ and $8$, the average speed is instead their harmonic mean, $2/(1/2+1/8)=16/5$. The useful choice depends on which quantity is being added: distances, times, or logarithms of growth factors.