Harmonic Mean

Harmonic Mean

Mean is an important concept in measures of central tendency. Measures of central tendency give the measure for the center of the data. We have different types of measures of central tendency those are Mean, Median and Mode. Mean is classified into three parts those are Arithmetic Mean, Geometric Mean and Harmonic Mean. Arithmetic Mean is simply the ratio of sum of observations and the number of observations. Geometric Mean is the nth root of the product of the observations, where ‘n’ is the number of observations. What is Harmonic Mean? Harmonic Mean Definition is the reciprocal of arithmetic mean of the reciprocal of the observations. Depends on the situation we have to know which mean is correct. We have relation among these three means, that is, Arithmetic Mean = Geometric Mean = Harmonic Mean. Harmonic Mean Formula can be described as

Weighted Mean is useful in some cases where each
observation do not have an equal importance. In general arithmetic mean we are giving equal importance to each observation but this is not always the case. When all the observations are not equally important then we have to use weighted arithmetic mean. In weighted arithmetic mean we do not take sum of the observation we multiply the observations with respect to their corresponding importance. In Weighted Harmonic Mean is the reciprocal of weighted arithmetic mean of the reciprocal of observations.

Harmonic Means may not applicable in all cases if zero value present in the observations then reciprocal of zero do not exist, hence harmonic mean also do not exist. Harmonic Mean is useful when there are extreme values present in the data then it gives true picture of the average of the data. The Harmonic Mean is better average when the numbers are defined in a relation to some unit.

 For example in case of averaging speed Harmonic Mean is better measure than Arithmetic Mean. Suppose we have to find the average speed of a person travelling from place A to place B. If the person travelling with 10kmph in first hour and 15kmph in second hour then the average speed is the arithmetic mean. If the person travels first half distance with the speed 10kmph and remaining distance with the speed 15kmph then Harmonic Mean is better measure then arithmetic mean. Harmonic Mean is also called as sub- contrary mean. Harmonic Mean is useful in case of finding averages involving rates and ratios.