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)
}