Kalamaoo County

Environmental Health

GEOMETRIC MEAN

Environmental Health uses the geometric mean to estimate the 30-day average from all individual samples taken during five or more sampling events. The geometric mean is another way to average a set of values and is commonly used with bacterial water assessment, which often show a great deal of variability. One benefit the geometric mean has over the arithmetic mean is that it (geometric mean) reduces the effect of an occasional high or low value on the average.

Most spreadsheet and database applications can automatically calculate the geometric mean. Two methods to calculate the geometric mean, both which achieve the same result, can be used with a scientific calculator and are illustrated in the following examples:

Procedure #1:

  1. Multiply all the data values (sample results) together to get the product.
  2. Take the "nth" root of the product of the multiplication, where "n" is the number of values multiplied. If you multiply three (3) values together and get the result, take the 3rd root of the product. If you multiply ten (10) values together and get the result, take the 10th root of the product. This is the geometric mean.

      Example Calculation #1:
    • With the following sample data results of 38, 95, and 52 colonies per 100 ml, calculate the geometric mean.
    • Multiply the three (3) data values together (38 * 95 * 52 = 187,720)
    • Take the 3rd root of 187,720 = 57.2580889011 colonies per 100 ml

Procedure #2:

  1. Add together the base 10 logarithms for the data values.
  2. Divide the sum by the number of values added.
  3. Take the antilog of the result of step #2. This will again be the geometric mean.

      Example Calculation #2:
    • With the following sample data results of 38, 95, and 52 colonies per 100 ml, calculate the geometric mean.
    • The base 10 logarithm of:
      38 is 1.57978359662
      95 is 1.97772360529
      52 is 1.71600334363
      5.27351054554 (sum)
    • Divide by the number of sample data values
      5.27351054554 / 3 = 1.75783684851
    • Antilog of 1.75783684851 = 101.75783684851 = 57.2580889013 colonies per 100 ml



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