Estimation of a Sample’s Mean and Variance from Its Median and Range

This page estimates the mean, variance, and standard deviation of a sample on the basis of the sample’s reported median and range according to the method devised by S.P. Hozo, B. Djulbegovic, and I. Hozo. In their 2005 paper on the method, the authors concluded by observing:

To proceed according to this method, enter the values for sample size, median, and low and high ends of the range into the designated spaces below and then click the «Calculate» button. Small-sample estimates based on the formulas shown above will be calculated for all samples, irrespective of size. For larger samples, the alternative estimates recommended by Hozo, et al. will also appear.

  Size of the sample

  Median of the sample

  Low end of the range of the sample

  High end of the range of the sample

   Reset         Calculate   
Small Sample

  Estimated mean of the sample

  Estimated variance of the sample

  Estimated standard deviation of the sample

S.P. Hozo, B. Djulbegovic, and I. Hozo, "Estimating the Mean and Variance from the Median, Range, and the Size of a Sample," BMC Medical Research Methodology 2005, 5:13

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