Comparison of several std deviation values each from different sample sizes

I have std deviation values for n different distributions, each consisting of a unique sample size. I observe that the std deviation values are inversely proportional to the sample sizes. Is there any good method to compare that n values or fit them with respect to some statistical rules?

Help is appreciated! Thanks :slight_smile:

You didn’t say how you estimated the variance. Could it be that you used the biased formula, and therefore, you see a downward bias of the estimated variance?

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Hi @StephanH,
I estimated the variance using the root function. h -> GetRMS()
Where h is the histogram that i have created for each sample set. Let me clarify you…
For example I have first set of 10 numbers: 5,4,6,5,4,5,5,4,6,6 (as we can see its mean is 5) . I for a histogram with these set of numbers and calculate the rms…
I have another set of 10 numbers: 20,22,21,19,18,20,20,21,22,21(whose mean is greater than the previous one) . I calculate the RMS value .
Similarly i calculate the rms value for 8 sets of numbers with different mean. What I observed is RMS is inversely proportional to the respective mean.

My question is: is there any way I can relate those 8 set of rms value / fit with any function?

Note that RMS != standard deviation. In your particular case, however, the function is just named poorly, so it actually computes the standard deviation (not the variance).

Next, please understand that it’s not possible for us to guess a function for you. Only you know where those numbers come from. Unless you can describe the process that generates the numbers, there is no reasonable way that we could propose a function.
Finally, also note that the sample size and the standard deviation are in general not correlated. See e.g. this:

{5, 5, 5, 5, 5, 5}. StdDev = 0, Sample size = 6
{0, 100}. StdDev = sqrt(5000) = 70, Sample size = 2

Thank you @StephanH.

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