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In some clinical studies, researchers may report the five number summary(including the sample median, the first and third quartiles, and the minimumand maximum values) rather than the sample mean and standard deviation. Toconduct meta-analysis for pooling studies, one needs to first estimate thesample mean and standard deviation from the five number summary. A number ofstudies have been proposed in the recent literature to solve this problem.However, none of the existing estimators for the standard deviation issatisfactory for practical use. After a brief review of the existingliterature, we point out that Wan et al.'s method (BMC Med Res Methodol 14:135,2014) has a serious limitation in estimating the standard deviation from thefive number summary. To improve it, we propose a smoothly weighted estimator byincorporating the sample size information and derive the optimal weight for thenew estimator. For ease of implementation, we also provide an approximationformula of the optimal weight and a shortcut formula for estimating thestandard deviation from the five number summary. The performance of theproposed estimator is evaluated through two simulation studies. In comparisonwith Wan et al.'s estimator, our new estimator provides a more accurateestimate for normal data and performs favorably for non-normal data. In realdata analysis, our new method is also able to provide a more accurate estimateof the true sample standard deviation than the existing method. In this paper,we propose an optimal estimator of the standard deviation from the five numbersummary. Together with the optimal mean estimator in Luo et al. (Stat MethodsMed Res, in press, 2017), our new methods have improved the existing literatureand will make a solid contribution to meta-analysis and evidence-basedmedicine.

How to estimate the sample mean and standard deviation from the five number summary?