# What are the differences between arithmetic mean, geometric mean and harmonic mean. [closed]

I mean to say can they ever be equal and what are other differences.

• Welcome to MSE! They are all equal when the things you're averaging are all the same. What kinds of "differences" are you looking for? May 6 at 16:14
• Try to see what happens if they are equal. If $\frac {a+b}2 = \sqrt{ab}$ what happens? What if $\frac {a+b}2 = \frac 1{\frac {\frac 1a + \frac 1b}2}$ or if $\frac 1{\frac {\frac 1a + \frac 1b}2}=\sqrt {ab}$? May 6 at 20:55

## 1 Answer

Arithmetic mean is when you sum them and divide by the number of numbers.

Geometric mean is when you multiply them and take the $$n$$th root when there are $$n$$ numbers.

Harmonic mean is when you take the multiplicative inverse of each number, take the arithmetic mean of those, and then take the multiplicative inverse of your answer.

I suggest trying out several small examples and comparing. For example, $$\{1,2,3\}$$, or $$\{2,2,2\}$$, or $$\{3,6,12\}$$.

• Sir, i know this and i have already tried it for several small examples to differentiate themselves, but I want to know what is exactly true for themselves even if there is more numbers than 1000 or 10000. May 7 at 20:50
• Have you checked out Wikipedia on harmonic mean or mean? May 7 at 20:53