Question

Another type of mean, known as the geometric mean, is defined as:

a) The sum of values divided by the number of values.
b) The square root of the product of values.
c) The reciprocal of the arithmetic mean.
d) The median of the values.

Answer 1

The geometric mean, distinct from the arithmetic mean, is calculated by multiplying all values together and taking the nth root of the product, where n is the number of values.

Step-by-step explanation:

The geometric mean is a type of mean that measures the central tendency of a set of numbers in a multiplicative fashion, in contrast to the arithmetic mean, which operates additively. The arithmetic mean is the common type of average most people are familiar with, and it involves adding all the numbers in a set together and then dividing by the count of those numbers. However, the geometric mean is calculated differently. Specifically, you calculate the geometric mean by multiplying all the numbers together and then taking the nth root of the resulting product, where n is the number of values in the set.

To provide an example, if we have a set of numbers [2, 8, 32], the geometric mean is calculated by multiplying 2*8*32 to get 512 and then taking the cube root (since there are 3 numbers) of 512, which results in 8. The geometric mean is particularly useful in situations where the numbers are in different ranges or are exponentially related to one another.