### CFA Practice Question

Which of the following is correct, if all the data are positive?
A. harmonic mean > arithmetic mean > geometric mean
B. harmonic mean < arithmetic mean < geometric mean
C. harmonic mean < geometric mean < arithmetic mean

User Comment
visiblebob These are the reverse of alphabetical.
spenja Thanks visiblebob. I didn't spot that.
trini01 Great memory trick!
Merke What if "all data are NEGATIVE"?
Is there any trick with that?
fmhp A>G>H
maria15 If it's negative, shouldn't it be A<G<H?
birdperson geometric means blows up with negative numbers because you can't take the square root of a negative... i don't think the geometric mean can every be negative...
adamrej guys, if you don't know this one by heart then just check for two numbers, like 1,2:

AM = 1.5
GM=sqrt(2) = 1.414
HM=1.33

Voila!
CalebMast The GM makes sense - formula for HM slightly harder.
next456 Consider the function f(n) = ((x^n+y^n+z^n)/3)^(1/n),
when n = -1, it is HM,
when n = 0, it is GM,
when n = 1, it is AM.

This function f(n) is an increasing function of n