Standard Article


  1. W. Smith

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15085

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Smith, W. 2005. Mean. Encyclopedia of Biostatistics. 5.

Author Information

  1. West Tisbury, MA, USA

Publication History

  1. Published Online: 15 JUL 2005


The sample arithmetic mean is the average of a set of numerical measurements. For a random variable, the analog is the expectation. In a weighted mean, the individual observations may be given different weights before averaging, perhaps because they represent groups of different sizes. The geometric mean is obtained by averaging logarithms (of positive-valued measurements) and then taking antilogarithms. The harmonic mean is obtained by taking reciprocals before averaging and then taking the reciprocal of the average. The relationship between the arithmetic, geometric, and harmonic means is described.


  • arithmetic;
  • geometric;
  • harmonic;
  • weighted;
  • lognormal;
  • skewed