Geometric Mean Given Frequencies

In this class, We discuss Geometric Mean Given Frequencies.

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The reader should have prior knowledge of geometric mean. Click Here.

Example 1:

The below table shows the data distribution.

GM = ((x1)^f1 * (x2)^f2 * . . . (xn)^fn)^(1/N)

N = 1 to nΣfi

GM = (1^2 * 2^3 * 3^2 * 4^1 * 5^2 * 6^2)

GM = 2.826

Example 2:

The geometric mean of ten observations was 16.2. 

One data value was recorded as 12.9 instead of 21.9.

Calculate the correct geometric mean.

GM = (x1, x2, . . . ,xn)^1/n

x1 = 12.9

GM = 16.2

x1′ = 21.9

GM’ = ((x1’/x1), x1, x2, . . . x10)^1/n

GM’ = (x1’/x1)^1/10 (x1, x2, . . . x10)^1/10

GM’ = (21.9/12.9)^1/10 * (16.2)

GM’ = 17.08