Is a geometric mean and a weighted average the same thing? If not, what's the difference?

Answer 1

geometric mean is the nth root of the product of n values

weighted average is an average that takes into account the proportional relevance of each component, rather than treating each component equally.

Answer 2

Mean Vs Geometric Mean

Answer 3

They are entirely different. The geometric mean of n numbers is the n-th root of their product. A weighted average is similar to an unweighted average, except that you multiply the elements by weights according to their perceived importance before adding them up, and you divide not by the number of items but by the sum of the weights.

Answer 4

No, they are not the same: the weighted average of two numbers a and b is (a+b)/2; the geometric mean of these two numbers is sqrt(a*b).

Answer 5

Geometric mean pertains to geometry with various legs of similar triangles. You'd need a geometry book to see it, words don't suffice. Weighted average means the average has been tweaked - like chucking out suspect data, or adding bias for a particular reason. Least this is as much as I can remember, been out of math for quite awhile.

Answer 6

let a & b be two numbers..... then

the geometric mean = sqrt (a*b)

simple average = (a+b)/2

weighted average = (ma+nb)/(m+n) for some given weights m & n

please do this now: when is the geometric mean and average of two numbers the same?

Answer 7

A weighed average of x and y has the form
[1] ... WA = a x + b y
where a and b are positive numbers with a + b = 1.

The geometric mean of x and y are
[2] ... GM = sqrt (x y)

WA is defined even when x and y are negative; GM only works for positive values.

If x and y are known then GM = WA if you pick

a = sqrt y / (sqrt x + sqrt y)
b = sqrt x / (sqrt x + sqrt y)