Resources / Calculator
Median to Mean & SD Converter
Estimate a mean and standard deviation from a study that only reports median and range, or median and interquartile range — useful when pooling continuous outcomes that weren't all reported the same way.
These are standard statistical approximations for when only median-based summaries are available — not exact conversions. For small samples or skewed distributions, the more precise Wan/Luo (2014/2018) methods may be worth using instead.
Why this matters for meta-analysis
Meta-analysis of continuous outcomes typically pools means and standard deviations. When some included studies report medians and ranges or interquartile ranges instead (common with skewed data like length of stay or pain scores), you need a way to estimate the missing mean and SD before pooling — otherwise those studies have to be excluded or handled narratively.
This tool uses two standard approximations:
- Median & range: Hozo, Djulbegovic & Hozo (2005) — mean ≈ (min + 2×median + max) / 4, SD ≈ range / 4.
- Median & IQR: assuming an approximately normal distribution — mean ≈ (Q1 + 2×median + Q3) / 4, SD ≈ (Q3 − Q1) / 1.35.
Both are approximations that work best when the underlying distribution is roughly symmetric. For skewed data or small sample sizes, consider the more precise sample-size-adjusted methods from Wan et al. (2014) and Luo et al. (2018), or get help from our biostatistics team.
Need help pooling mixed summary statistics?
Our team handles studies that report means, medians, and everything in between — with a documented, defensible conversion method for each.
See Meta-Analysis Support