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median variance

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Contributor
Posts: 36

median variance

Hello, I am wondering weather it is possible to calculate variance for median for none sampling data. Thank you!
Respected Advisor
Posts: 4,920

Re: median variance

Please give a formula/equation/reference for "variance for median for none sampling data"?

PG
Contributor
Posts: 36

Re: median variance

I do not know a formula for variance of a median. So I am wondering whether it is even exist. I know how to calculate variance for a mean but not for a median.

Respected Advisor
Posts: 4,920

Re: median variance

If you are looking for robust estimators of dispersion (scale), check out the MAD, Sn and Qn estimators available in proc UNIVARIATE. 

PG
Contributor
Posts: 36

Re: median variance

Thank you for a suggestion. I will check it out.

SAS Super FREQ
Posts: 3,752

Re: median variance

You can search for "distribution of sample median" or "sampling distribution of median" to find references. Basically, the standard error of the median will depend on the distribution of the underlying data, so there is not a general formula. If you assume that the data are normally distributed, you can write down an asymptotic formula: stderr_median = 1.253*sigma / sqrt(n), where sigma is standard devition of the normal population and n is the sample size.

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