Median to Mean Conversion

Converts median-based summary statistics into estimated mean and standard deviation — invaluable when a paper reports median (with quartiles or range) but your meta-analysis needs mean and SD.


Inputs

  • Sample size (n)
  • Median
  • Either Q1 and Q3 (quartiles), or Min and Max

Methods used (Hozo et al., 2005)

Available data Mean estimate SD estimate
Median + Q1 + Q3 (Q1 + median + Q3) / 3 (Q3 - Q1) / 1.35
Median + Min + Max Hozo formula based on min, median, max, and n Hozo range-based SD formula

The (Q3 - Q1) / 1.35 approximation comes from the fact that for a normal distribution, the IQR is approximately 1.35 standard deviations.

These estimates assume approximate normality; for highly skewed data they are less accurate.

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