# Estimating the mean and standard deviation from the median and the range

[This article was first published on

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**Statistical Reflections of a Medical Doctor » R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

While preparing the data for a meta-analysis, I run into the problem that a few of my sources did not report the outcome of interest as means and standard deviations, but rather as medians and range of values. After looking around, I found this interesting paper which derived (and validated through simple simulations), simple formulas that can be used to convert the median/range into a mean and a variance in a distribution free fashion. With

- a = min of the data
- b = max of the data
- m = median
- n = size of the sample

the formulas are as follows:

**Mean **

**Variance **

The following R function will carry out these calculations

f<-function(a,m,b,n)

{

mn<-(a+2*m+b)/4+(a-2*m+b)/(4*n)

s=sqrt((a*a+m*m+b*b+(n-3)*((a+m)^2+(m+b)^2)/8-n*mn*mn)/(n-1))

c(mn,s)

}

To

**leave a comment**for the author, please follow the link and comment on their blog:**Statistical Reflections of a Medical Doctor » R**.R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.