The harmonic mean is a type of average used in mathematics and statistics. It is one of the Pythagorean means and is sometimes appropriate for situations when the average rate is desired. The harmonic mean is calculated by dividing the number of values in a data series by the sum of the reciprocals of each value in the series. It is the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. The harmonic mean is used when there is a necessity to give greater weight to the smaller items, and it is applied in the case of times and average rates. The harmonic mean is often used to calculate the average of ratios or rates because it equalizes the weights of each data point. The formula to define the harmonic mean "HM" is given as follows: If x1, x2, x3,…, xn are the individual items up to n terms, then, Harmonic Mean, HM = n / . The harmonic mean is related to the other Pythagorean means, as seen in the equation below:
$$\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}$$
The harmonic mean is useful in calculating the average of rates and ratios. It is the most appropriate measure for ratios and rates because it gives less weightage to the large values and more weightage to the small values to balance the values correctly. In finance, the harmonic mean is used to determine the average for financial multiples such as the price-to-earnings (P/E) ratio. The harmonic mean is also good at handling large outliers.
