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Appendix 6. Calculation of arithmetic and geometric means

There are several methods for measuring the central tendency of a set of numbers.

One method is to calculate the arithmetic mean. To do this, add up all the values and divide the sum by the number of values. For example, if there are a set of “n” numbers, add the numbers together for example: a + b + c + d and so on. Then divide the sum by “n”.

One problem with the arithmetic mean is that its value will be influenced disproportionately by a single extreme value.

Another method is to calculate the geometric mean. To do this, multiply the values together and then, if there were “n” numbers, take the “nth” root. Single extreme values then have less influence.

This method is particularly useful when results are recorded in logarithmic notation. To multiply you only have to add the log indices. To approximate the geometric mean, you take the arithmetic mean of the log indices.

Worked Example

You have recorded the following set of values in a serological test. To calculate the arithmetic mean, you must transform these to real numbers.

23 = 8

24 = 16

24 = 16

26 = 64

Calculation of the geometric mean = 4Ö(8 × 16 × 16 × 64) = 4Ö(131072) = 19

Calculation of the geometric mean using the log indices =

The geometric mean is then = 24.3 = 19.7

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