# Properties of different types of means: geometric, harmonic, arithmetic, exponential

• Apr 29th 2011, 09:48 AM
Alonso
Properties of different types of means: geometric, harmonic, arithmetic, exponential
Dear all,

I am facing an interesting problem: I have a number of datasets containing observations. Each dataset has observations, whose distribution is skewed. Some datasets are left-skewed, for example:

.1, .1, .6, .76,.8,.98,.99,.99,.99,1

while other are right-skewed:

.01,.01,.05,.07,.08,.2,.2,.4,.4,1

Is there a measure of central tendency that works as follows: if the sample distribution is left-skewed, points at the left side receive more weight than points at the right side in the final "average". On the other hand, when the distribution is right-skewed, points at the right side receive more weight than points at the left side. More weight means "contribute more" in the "overall mean"

I have tested the geometric, harmonic, arithmetic and exponential means, but none of them seem to work well in my case.

Any tips are appreciated!

Alonso

P.S. Median is not appropriate in my case (biological reasons).
• Apr 29th 2011, 02:16 PM
pickslides
Whynot just apply the arithmetic mean if you have no outliers?
• Apr 29th 2011, 03:01 PM
Alonso
Because the arithmetic mean gives more weight for the largest values.
• Apr 30th 2011, 01:14 AM
SpringFan25
i dont know the answer but out of interest, why do you think a measure with the properties you mentioned would be useful?