how do you find the geometric mean and harmonic mean of:
2/3, 3/4, and 9/36?
2006-12-04 09:43:22 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Geometric mean = nth root of the product of n numbers.
I'm guessing when you said 2/3 you meant "find the geometric mean of 2 and 3", rather than finding the geometric mean of those three fractions.
In that case, the geometric means are sqrt(2*3), sqrt(3*4) and sqrt(9*36) respectively.
The harmonic mean of n numbers is n/(1/a + 1/b + ..).
So we add up their reciprocals, and divide that into n.
In this case, 2/(1/2 + 1/3) = 12/5, 2/(1/3 + 1/4) = 24/7, 2/(1/9 + 1/36) = 72/5.
(If you did intend to find the means of those three fractions, they would be:
G.M: cuberoot(2/3 * 3/4 * 9/36) = 1/2
H.M: 3/(3/2 + 4/3 + 36/9) = 18/41.)
2006-12-04 09:52:55 · answer #1 · answered by stephen m 4 · 3⤊ 0⤋
precise but well explained...thanx
2014-12-30 20:43:09 · answer #2 · answered by ? 1 · 0⤊ 0⤋