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

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

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Suggested answer

The geometric mean is found by multiplying all the *n* observations together
and then taking the *n*th. 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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