Applications of Arithmetic mean, Harmonic mean and Geometric mean In case where one deals with tabulated frequency distributions, which type of data is more suited to arithmetic mean, geometric mean and harmonic mean? I know how to calculate these means. However, I am confused which type of data requires arithmetic mean, or geometric mean or harmonic mean as the best average.

Datasets following a linear regression are most easily summarised by the arithmetic mean. If the fit is exponential (the values span several orders of magnitude), the geometric mean is a better choice, and reciprocal regression (as is common with speeds and other rates) is usually explained with a harmonic mean.

In short, the equation your data values fit determines what type of average is most appropriate.