If G is the geometric mean, H is the harmonic mean, and A is the arithmetic mean, their connection is given by. The following are the formulae for three different classifications of means: Pythagorean means are three means in statistics that include arithmetic, geometric, and harmonic means. Relationship Between Arithmetic Mean, Geometric Mean and Harmonic Mean Individual values are represented by a1, a2.an. Where w denotes weight and x denotes the variable If x1, x2., xn are n items with corresponding frequencies f1, f2., fn, the weighted harmonic mean is: If the frequencies "f" are assumed to represent the weights "w," the harmonic mean is computed as follows: It is analogous to the basic harmonic mean. Weighted harmonic mean is a subset of harmonic mean in which all weights are equal to one. It is also used in the calculation of Fibonacci sequences.In the financial industry, the harmonic mean is important for calculating average multiples such as the price-earnings ratio.Under specific conditions, determining average pricing, average speed, and so on.Here are some of the major uses of Harmonic Mean: The harmonic mean has minimal worth when contrasted with the mathematical mean and the number arithmetic mean i,e AM > GM > HM. On the off chance that every one of the perceptions taken are constants, say c, the harmonic mean of the perceptions is likewise c. Harmonic Mean, HM = n/ Properties of Harmonic Mean
On the off chance that x1, x2, x3,…, xn are the singular things up to n terms, then, at that point, Since the harmonic mean is the proportional of the normal of reciprocals, the equation to characterize the consonant signify "HM" is given as follows: