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 Contributed Comments 10
| 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 |