Estimating the sample variance from the sample size and range

For meta-analysis studies and systematic reviews, it is important to pool the data from a set of similar clinical trials. To pool the data, one needs to know their SD. Many trial reports, however, contain only the median, the minimum and maximum values, and the sample size. It is therefore important to be able to estimate the SD S from the sample size n and range r. For small n ≤ 100, we improve existing estimators of r/S, the "divisor," denoted by $\xi \left(n\right)$ . This in turn yields improved estimators of the SD in the form $\hat{S}=r/\hat{\xi }\left(n\right)$ on simulated as well as real datasets. We provide numerical values of the proposed estimator as well as approximation by a simple formula $3\sqrt{\ln \left(n\right)}-1.4025$ . Furthermore, for large n, we provide estimators $\hat{\xi }\left(n\right)$ of the divisor $\xi \left(n\right)$ for the normal, exponential, and other bounded and unbounded distributions.