I think this is simple

In cells C1 put the formula
=average(A1:A1000)

the copy this formula to cells C2 - C25.
C1 to c25 will be your array of averages.

"hmm" wrote:

I have a column of data comprising a series of 25 arrays. I would like to
generate an array whose elements are the average of the corresponding
positions in each of the 25 arrays.

Suppose, for example, the first array is in cells A1 to A1000, the 2nd in
A1001 to A2000, etc. What formula would give me the average of A1, A1001,
A2001, ..., A24001?