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mean





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

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 nth 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.


Related category

   • APPROXIMATIONS AND AVERAGES