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?