MATLAB: Calculation of mean signal frequency

fftfrequency

Hi everyone,
I'm trying to perform an analysis in the frequency domain, but I'm confused regarding how to obtain the PSD signal.
Currently, I'm using the following to obtain the PSD:
L = length(data);
% Compute Fast Fourier Transform
Y = fft(data);
% Compute the two-sided spectrum P2
P2 = abs(Y/L);
% Compute the single-sided spectrum P1 based on P2
P1 = P2(1:ceil(L/2)+1);
P1(2:end-1) = 2*P1(2:end-1);
power = P1;
% Define the frequency domain axis
frequencies = fs*(0:ceil(L/2))/L;
I have tested this with the following signal:
fs = 200;
x = 0:1/fs:20
data = sin(2*pi*5*x);
And I get the following PSD:
I'm trying to calculate the mean frequency using the following formula:
mean_frequency = sum(power.*frequencies)/sum(frequencies)
Where I obtain 
mean_frequency = 5.0587e-04
which is obviously wrong. However, when I use MATLAB's meanfreq function, I get meanfreq(data, fs) = 4.999Hz, which is the expected.
Can please anyone tell me what I'm doing wrong? After this I want to perform a complete analysis in the frequency domain (e.g, median frequency, total power, etc) and I need to make sure my PSD data is correct.
Many thanks for your attention,
Diogo

Best Answer

There are two small errors.
Correcting them: 
P2 = abs(Y/L).^2;                                           % Power = Amplitude^2
and: 
mean_frequency = sum(power.*frequencies)/sum(power)         % Divide By Sum Of Power
producing: 
meanfreq =
          4.99913568484097
.
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