Question

What is the difference between harmonic mean and arithmetic mean?

Answer 1

The difference between harmonic mean and arithmetic mean:

Arithmetic Mean	Harmonic Mean
Arithmetic mean is the sum of a collection of numbers divided by the number of numbers in the collection.	The harmonic mean is the reciprocal of the average of the reciprocals of the data values.
For a data set $a_1,a_2,a_3,.....,a_n$, the arithmetic mean is, $\mathbf{A}\mathbf{.}\mathbf{M}\mathbf{}\mathbf{=}\mathbf{}\frac{{\mathbf{a}}_{\mathbf{1}}\mathbf{+}{\mathbf{a}}_{\mathbf{2}}\mathbf{+}{\mathbf{a}}_{\mathbf{3}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{a}}_{\mathbf{n}}}{\mathbf{n}}$	For a data set $a_1,a_2,a_3,.....,a_n$, the harmonic mean is $\mathbf{H}\mathbf{.}\mathbf{M}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}}{\frac{\mathbf{1}}{{\mathbf{a}}_{\mathbf{1}}}\mathbf{+}\frac{\mathbf{1}}{{\mathbf{a}}_{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{{\mathbf{a}}_{\mathbf{3}}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}\frac{\mathbf{1}}{{\mathbf{a}}_{\mathbf{n}}}}$

Hence, the difference is clearly explained.