There are numerous examples in different research fields where the use of the
geometric mean is more appropriate than the arithmetic mean. However, the
geometric 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 a
single number; yet, the geometric mean of a data set with at least one zero is
always zero. As a result, the geometric mean does not capture any information
about the non-zero values. The purpose of this short contribution is to review
solutions proposed in the literature that enable the computation of the
geometric mean of data sets containing zeros and to show that they do not
fulfil the `recovery' or `monotonicity' conditions that we define. The standard
geometric mean should be recovered from the modified geometric mean if the data
set does not contain any zeros (recovery condition). Also, if the values of an
ordered data set are greater one by one than the values of another data set
then the modified geometric mean of the first data set must be greater than the
modified geometric mean of the second data set (monotonicity condition). We
then formulate a modified version of the geometric mean that can handle zeros
while satisfying both desired conditions
