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If I have two frequencies:

$f_1 = 20\text{ Hz}$

$f_2 = 40\text{ Hz}$

the mean between them should be

$f_\text{mean} =\frac{20+40}{2}=30\text{ Hz}$

How come that if I calculate their periods' mean

$\frac{\frac{1}{20}+\frac{1}{40}}{2} = \frac{3}{80}\neq \frac{1}{f_\text{mean}} $

the value is different from $1/f_\text{mean}$ ?

Where am I getting wrong?

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    Y$e$s, sorry about that2012-05-17

1 Answers 1

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You aren't going wrong. There is no reason to think that the average of the reciprocals of a set of numbers is the reciprocal of the averages of the original numbers. In fact I think since 1/x is convex the Jensen inequality shows that it has to be different.