Mean, Median, and Average Values of Variables

Abstract

The data analyst often faces the question of what is the “best” value to report from N measurements of a random variable. In this chapter we investigate the use of the linear average, the weighted average, the median and a logarithmic average that may be applicable when the variable has a log-normal distribution. The latter may be useful when a variable has errors that are proportional to their measurements, avoiding the inherent bias arising in the weighted average from measurements with small values and small errors. We also introduce a relative-error weighted average that can be used as an approximation for the logarithmic mean for log-normal distributions.