Clinical Biostatistics: Geometric mean length of hospital stay exercise, suggested answer 2

2. What is a geometric mean and how was it calculated?

Suggested answer

The geometric mean is found by multiplying all the n observations together and then taking the nth. root. For example, the geometric mean of 4 and 9 is 6, found by multiplying 4 by 9 to give 36 and taking the square (or second) root.

The geometric mean is usually smaller than the arithmetic mean. For 4 and 9 this is (4 + 9)/2 = 6.5.

In practice, we calculate it using a logarithmic transformation of the data. If we find the mean on the log scale, taking the antilog of this mean gives us the geometric mean.

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Last updated: 31 July, 2006.