When can I use a median (IQR) in place of a mean ± SD? Or is it always acceptable?

It is best when a study reports the mean ± SD, but now and then you will meet a median with an interquartile range (IQR). Do this:

1. Mean: use the median directly as the mean. For a closer estimate, Wan and colleagues give a formula that uses the first quartile, the median and the third quartile.

2. SD: divide the IQR by 1.35. This holds when the sample is reasonably large and the data are roughly normally distributed. When the data are clearly skewed, the IQR is not a reliable basis for estimating an SD.

If you prefer not to calculate by hand, the online calculator from Wan's research group does it for you: enter n, Q1, the median and Q3.

https://www.math.hkbu.edu.hk/~tongt/papers/median2mean.html

Note: the familiar "divide by 4, divide by 6" rules come from Hozo and colleagues. They apply to the range (maximum minus minimum), not to the IQR.

References

• Higgins JPT, Li T, Deeks JJ (editors). Cochrane Handbook for Systematic Reviews of Interventions, Chapter 6, Section 6.5.2 (last updated August 2023).
• Wan X, Wang W, Liu J, Tong T. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol. 2014;14:135.
• Hozo SP, Djulbegovic B, Hozo I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol. 2005;5:13.