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.


arithmetic 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.


geometric mean

The geometric mean of n values is the nth root of the product of the values. In the case of two numbers, a and b, the geometric mean is √(ab).

Thus the geometric mean of the numbers 4 and 9 is √(4 × 9) = √36 = ±6. If the numbers are 3, 8, and 10 then the geometric mean is (3 × 8 × 10)1/3 or the cube root of 240.


harmonic mean

The harmonic mean is the reciprocal of – in other words, 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].


weighted mean

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.



A different kind of average is median, which is generally the center term when a group of numbers are ordered by size.the median is the value of the middle member of a set of numbers when arranged in order from smallest to largest. For example, in the series 2, 3, 7, 9, 10, the median is 7. With an
even number of items, the median is taken to be the arithmetic mean of the two middle items. Thus, in the series 2, 3, 7, 8, the median is 5.



The words 'mean' and 'median' both come from the same origin – the Indo-European root medhyo meaning 'middle'.