Essentailly what I am interested is to solve Equation 10.25 in the following link <http://books.google.co.uk/books?id=Hwb5D60vb5IC&pg=PA701&lpg=PA701&dq=%22mean+angular+frequency%22&source=bl&ots=dSH6fzeZNC&sig=GB5J8nwpLCIULGhAHZLAm0RxgLM&hl=en&ei=NubNSpKqO92NjAeqwKmHBA&sa=X&oi=book_result&ct=result&resnum=9#v=onepage&q=%22mean%20angular%20frequency%22&f=false> ie. solve for the mean angular frequency. Let's call it x' where x'=integral(x*y(x).dx)/integral(y(x).dx) % Equation 10.25 where y(x) is the spectral density and x is the angular frequency. I have data for the spectral density values for a given angular frequency y=[6.2770 10.5137 14.8385 19.2196 21.5972 19.6632 15.2690 10.9238 6.5569] x=[ 2.6097 2.6158 2.6259 2.6314 2.6501 2.6615 2.6633 2.6654 2.6659] How can I solve for x' using the above data in Matlab? My understanding is that the numerator is essentially: sum[x*y(x)] for the given values of x and y (ie a weighted form ). therefore I have numerator=x.*y; the bottom is the integral so i tried using the matlab function trapz(x,y) to calculate that as well. denominator =trapz(x,y); therefore x'=numerator/denominator But the answer I get is incorrect. I am not sure where my mistake is. Any help will be much appreciated!