Harmonic Mean


The reciprocal of the average of the reciprocals of two or more quantities. If the quantities are named a and b, their Harmonic Mean is:


In Information Retrieval, F1 is the Harmonic Mean of Recall and Precision. The Harmonic Mean, unlike the more common arithmetic mean (i.e., average), falls closer to the lower of the two quantities. As a summary measure, a Harmonic Mean may be preferable to an arithmetic mean because a high Harmonic Mean depends on both high Recall and high Precision, whereas a high arithmetic mean can be achieved with high Recall at the expense of low Precision, or high Precision at the expense of low Recall. 1


  1. Maura R. Grossman and Gordon V. Cormack, EDRM page & The Grossman-Cormack Glossary of Technology-Assisted Review, with Foreword by John M. Facciola, U.S. Magistrate Judge2013 Fed. Cts. L. Rev. 7 (January 2013).