Some properties of the geometric mean and its use in water quality standards

The geometric mean is often used to express acceptable levels of fecal coliform counts in federal and state water quality criteria or standards. The expected value of the geometric mean is shown to be a function of the sample size and to be very sensitive to the skew as well as to the form of the underlying distribution function. Implications of these findings are discussed with regard to standards. In particular, it is noted that great care must be taken in specifying the minimal sample size to be used.