calculating mean and SD from median, IQR and sample size

[Shripada Rao]

Dear friends, is there a way we can calculate mean and standard deviation of the data using median, interquartile range and sample size in stata? Thank you for your help

[Clyde Schechter]

Well, if the distribution in question has a known parametric form, there are formulas that can be used. For example, if the distribution is Gaussian, then the mean equals the median, and the interquartile range corresponds to 1.35 standard deviations. Similar things can be worked out for all of the "usual suspect" distributions. You can find the formulas in any textbook of mathematical statistics, or, for that matter, you can look them up in Wikipedia. (For some of the distributions you may not find direct formulas linking these things, but you will find formulas expressing both sets of statistics to some other parameterization of the distribution, which you can then, with a little algebra, use to get the correspondence you want.)

But if the data don't fit a parametric distribution, or you don't know which one, then there is no way to calculate mean and SD from median and IQR.

[Shripada Rao]

Hi Clyde, thank you for this information.

[Tiago Pereira]

You can use these approximations, which work very well provided that the sample sizes are not too small:
https://www.math.hkbu.edu.hk/~tongt/...dian2mean.html

You can use the website if you have few estimates. Implementation in Stata should be easy.

[Bruce Weaver]

An just in case anyone missed it, notice the distinction between calculating (which is mentioned in the topic) and estimating or approximating.