The sum of the kernel density values is not 1?

>> x = [randn(30,1); 5+randn(30,1)];
>> [f,xi] = ksdensity(x);
>> sum(f)

ans =

5.5376


I ran the ksdensity function in MATLAB above. After getting the density values, I summed them up. I've got 5.5376, but I expected 1. What am I missing here? Is there any good introductory book that explains the mechanics of the kernel density estimation in line with the ksdensity function?

• This question seems to come down to a misunderstanding of densities, which is addressed at stats.stackexchange.com/questions/4220. Does that solve your problem? – whuber Oct 6 '14 at 23:32
• Thank you very much, whuber. Confusing, but I will dig in. – Bill TP Oct 6 '14 at 23:44
• You appear to be summing the height of the density at some collection of values. Why would that sum to 1? – Glen_b Oct 7 '14 at 1:55

trapz(xi, f) should return something close to 1.