MATLAB: Overestimation of mean with trapz

approximate integralintegrationmean valuenumerical integrationtrapz

Hi,
I'm using trapz(x,y) to find the mean value of a portion of a signal.
x = [0.3 0.3 0.3 0.4 0.5 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.2 1.3 1.4 1.4 1.5 1.5];
y = [14.0 15.8 15.8 16.3 19.7 23.5 25.2 27.1 28.4 29.1 30.3 30.6 30.6 30.5 30.5 30.4 30.4 30.4 30.3];
The maximum value in y is 30.6. However, trapz(x,y) = 32.3.
Why is the mean value estimated by trapz greater than the maximum value of the dataset? I thought maybe the spacing was too coarse and tried interpolating on a much finer grid, but the trapz mean still exceeded the maximum value of y.
Thanks for any help!

Best Answer

The mean is defined as the integral of ‘y(x)’ from ‘x=a’ to ‘x=b’ divided by ’(b-a)’:
trapz_mean = trapz(x,y)/(max(x)-min(x));
trapz_mean =
    26.9292
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