I want to compute the standard deviation of the averages of several
random samples of data. Suppose the random samples are in A1:A10,
B1:B10, C1:C10, etc.

Of course, I could compute the averages in row 11 (e.g.
=AVERAGE(A1:A10) in A11), then compute STDEV(A11:H11) if I have 8
samples. But I would like to avoid storing the intermediate averages.

Ostensibly, I could compute
STDEV(AVERAGE(A1:A10),AVERAGE(B1:B10),...). But that works only for
up to 30 samples.

I would like to have an array formula that effectively computes
STDEV({AVERAGE(A1:A10), AVERAGE(B1:B10),..., AVERAGE(ZZ1:ZZ10)}).

How can I do write that array formula?