# Arithmetic vs Geometric Mean

There are verbal suggestions everywhere on when one should use a geometric average or when an arithmetic average should be preferred, but I can't find any formal statistical treatment of this question. Is it possible to formally test which one of these averages should be used for a particular sample?

• What do you mean and want by formally test? A numeric example with verbal moral won't suit? – ttnphns Mar 13 '14 at 5:58
• No, there aren't any formal tests of this. And it isn't the particular sample that matters as much as what the variable is and what you are trying to get. There are ways to show that the arithmetic mean gives wrong results in some cases. – Peter Flom Mar 13 '14 at 9:55
• Thanks for the response. Shouldn't distribution of the data have a bearing on which kind of a mean should be used? For example, is it wrong to sugegst using arithmetic mean if the data is normally distributed and geometric mean if its log is normally distributed? If such claims can be made, why can't we have a statistical test for it? – user41838 Mar 14 '14 at 3:50
• This has come up before. – Dimitriy V. Masterov Mar 16 '14 at 5:13