The geometric mean of five observations is the
A) same as their weighted mean.
B) same as their mean.
C) square root of the product of the 5 observations.
D) fifth root of the product of the 5 observations.

Question

Quizplus · Accepted Answer

The geometric mean of a set of numbers is defined as the nth root of the product of n numbers. In this case, we have 5 observations, so the geometric mean is the fifth root of the product of the 5 observations. Therefore, the correct answer is D. The weighted mean is a different type of average that takes into account the weights assigned to each observation, so A is incorrect. The mean is simply the sum of the observations divided by the number of observations, which is not the same as the geometric mean, so B is incorrect. The square root of the product of the 5 observations is the square root of 5 numbers multiplied together, which is not the same as the definition of the geometric mean, so C is also incorrect.

The Geometric Mean of Five Observations Is the