The geometric mean of the numbers 9, 12 and 16 is:

The geometric mean of 9, 12 and 16 is the cube root of their product 1728, which equals 12.

Multiplying 9 by 12 gives 108, and 108 by 16 gives 1728.

Since twelve cubed is 1728, its cube root returns exactly 12.

The value 12.33 is in fact the arithmetic mean of the three numbers, set as a distractor.

The figures 11.66 and 12.66 are neither the correct geometric nor arithmetic mean.

For positive numbers the geometric mean never exceeds the arithmetic mean, here 12 against 12.33.