1. ## index of variability

Hi
I have objects and each object have given precentages of their appearances in different situations. For example:
object 1
20%
40%
30%
5%
5%
object 2
90%
10%
etc.
I would like to calculate a single numerical value describing the variability of the objects so that I could easily compare them. What would be the most proper way to do calculate this variability value.

2. ## Re: index of variability

If the problem is so generic, a good old standard deviation may be sufficient. If there are other aspects of the problem, please let us know... In particular, if there are reasons to believe that the two objects offer similar performance, then the test statistic from a two-sample Kolmogorov-Smirnov test might be good.

3. ## Re: index of variability

Thank you for suggestion but standard deviation is actually not good.
For example:
100% vs(2x50%)vs(10x10%)
In all cases the standard deviation equal to all (it is exactly zero) (in case of 100% you can not calculate that) although the variability is very different.

I am not sure about test statistic from a two-sample Kolmogorov-Smirnov test.

First, as I will have at least 3000 object I want to compare then I should compare them one by one with same thing.
Second I am not sure against what should I compare things.

I compared some example objects against object (100x1%). If I understood correctly then test statistic from a two-sample Kolmogorov-Smirnov test is maximum difference of two compared cumulative distributions.
I got following results:
60%, 4*10% - 0.4
60%, 30%, 10% - 0.4
60%, 40% -0.4
Again all objects with clearly different variabilities are giving same numerical output which does not fulfill my need.
Even when I used for comparison some other distributions (mean 50% sdev 2-50) all objects where max percentage was 70% + additional percentage (eg 70%+30% vs 70%+30*1%) gave same result.

Does anybody have any other suggestions.

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