analyzing FFT data for mean frequency?

Question

I used numpy fft.fft to analyze some time series data (black) and generate a plot like the following:

From the FFT data (in red) i calculated mean frequency by multiplying x*y for each data point and dividing by the number of data points. Is this correct? or am i misunderstanding what the y-axis means.

if this is incorrect, how are mean and median frequency calculated, or are those not useful metrics?

Thank you for your time and consideration.

Answer 1

First of all you probably want to do this in terms of power not amplitude, so I would square the y axis. Also, to calculate the mean you multiply x*y at each data point, add them up, and at the end you divide by the total power, so the sum of all the y values.