# mean

When she told me I was average, she was just being mean.

– anonymous

The mean is a precisely calculated 'typical' value of a group of numbers. There a several
kinds of mean. The **arithmetic mean**, which is usually what
is meant when people talk about an average, is the sum of a set of values
divided by the number of values. For example, the arithmetic average of
3, 4, 7, and 10, is (3 + 4 + 7 + 10)/4 = 6.

The **geometric mean** of *n* values is the *n*th root of the product of the values.
For example, the geometric mean of 3, 8, and 10 is (3 × 8 × 10)^{1/3} or the cube root of 240.

The **harmonic mean** is the reciprocal
of, or one over, the mean of the reciprocals of the values. For example,
the harmonic mean of 3, 8, and 10 is 1/[(1/3 + 1/8 + 1/10)/3].

A different
kind of average is **median**, which is generally the center
term when a group of numbers are ordered by size. If there are an even number
of values then it is the arithmetic mean of the center two is the median.
The words "mean" and "median" both come from the same origin – the
Indo-European root *medhyo* meaning "middle."

If, in a set of observations, the observations are weighted according to
their relative reliability, the individual values are first multiplied by
weighting factors before they are summed and the mean taken; this is then
called a **weighted mean**.