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There are numerous examples in different research fields where the use of thegeometric mean is more appropriate than the arithmetic mean. However, thegeometric mean has a serious limitation in comparison with the arithmetic mean.Means are used to summarize the information in a large set of values in asingle number; yet, the geometric mean of a data set with at least one zero isalways zero. As a result, the geometric mean does not capture any informationabout the non-zero values. The purpose of this short contribution is to reviewsolutions proposed in the literature that enable the computation of thegeometric mean of data sets containing zeros and to show that they do notfulfil the `recovery' or `monotonicity' conditions that we define. The standardgeometric mean should be recovered from the modified geometric mean if the dataset does not contain any zeros (recovery condition). Also, if the values of anordered data set are greater one by one than the values of another data setthen the modified geometric mean of the first data set must be greater than themodified geometric mean of the second data set (monotonicity condition). Wethen formulate a modified version of the geometric mean that can handle zeroswhile satisfying both desired conditions.

Geometric mean extension for data sets with zeros