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**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

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**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 |