Then you want:
where is the location of the -th point and is the value there.
But note that we have now gone from a discrete distribution to a continuous one, and:
and if you wish to approximate this integral by a sum over a equispaced set of 's you have to multiply the sum by the spacing between the points:
and the sum should extent over a range containing most of the distribution (say from the smallest at which is defines to the largest such , )