https://statmd.wordpress.com/2015/annual-report/

## Archive for December, 2015

### My 2015 blogging report

December 29, 2015### Estimating the mean and standard deviation from the median and the range

December 3, 2015While 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)

}

Edit

Surfing around arxiv, I found another paper that handles additional scenarios and proposes alternative formulas