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

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    $\begingroup$ 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? $\endgroup$ May 6 at 16:14
  • $\begingroup$ 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 $\frac 1{\frac {\frac 1a + \frac 1b}2}=\sqrt {ab}$? $\endgroup$
    – fleablood
    May 6 at 20:55
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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 $\{3,6,12\}$.

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  • $\begingroup$ 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. $\endgroup$
    – Mehedi
    May 7 at 20:50
  • $\begingroup$ Have you checked out Wikipedia on harmonic mean or mean? $\endgroup$ May 7 at 20:53

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