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

December 3, 2015

(This article was first published on Statistical Reflections of a Medical Doctor » R, and kindly contributed to R-bloggers)

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  \bar{m} = \frac{a+2 m+b}{4} +\frac{a-2 m+b}{4 n}

Variance  \frac{1}{n-1} \Big(a^2+m^2+b^2+\frac{n-3}{2} \frac{(a+m)^2+(b+m)^2}{4}-n \bar{m} \Big)


The following R function will carry out these calculations



To leave a comment for the author, please follow the link and comment on their blog: Statistical Reflections of a Medical Doctor » R. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Search R-bloggers


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)