= Mean
{disambiguate=mathematics}
= Mathematical mean
{synonym}
A <mathematical mean> assigns a representative value to several quantities. A real mean of $x_1,\ldots,x_n$ 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.
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