Overestimation of mean with trapz

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!

Answer 1

[Star Strider]

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

[Emily]

Thanks! I thought the division by the range was implicit.

[Star Strider]

My pleasure!

In the mean function, it is. Calculating it using numerical (or symbolic) integration, it is not.