I have an array of 10 rows by 20 columns. Each columns corresponds to a data set that cannot be fitted with any sort of continuous mathematical function (it's a series of numbers derived experimentally). I would like to calculate the integral of each column between row 4 and row 8, then store the obtained result in a new array (20 rows x 1 column).

I have tried using different scipy.integrate modules (e.g. quad, trpz,...).

The problem is that, from what I understand, scipy.integrate must be applied to functions, and I am not sure how to convert each column of my initial array into a function. As an alternative, I thought of calculating the average of each column between row 4 and row 8, then multiply this number by 4 (i.e. 8-4=4, the x-interval) and then store this into my final 20x1 array. The problem is...ehm...that I don't know how to calculate the average over a given range. The question I am asking are:

1. Which method is more efficient/straightforward?
2. Can integrals be calculated over a data set like the one that I have described?
3. How do I calculate the average over a range of rows?