Question

Lets say I have a large set of data .

Then I can divide it into two find mean of those two and calculate the mean of the last 2 values I get.

a) Is this the mean of the original big quantity ?

b) Can I do this sort of method for calculating standard deviation ??

Answer 1

a) only if the sets you divide into are always the same size, meaning that the original set size must be a power of 2.

For example, the mean of {6} is 6, and the mean of {3,6} is 4.5, but the mean of {3,6,6} is not 5.25, it’s 5.

Certainly you could recursively divide into parts to calculate the sum, though, and divide by the total size at the end. Not sure if that does you any good.

b) no

For example, the s.d of {2} is 0, and the s.d. of {1} is 0, but the s.d of {1,2} is not 0.

Once you’ve calculated the mean of the whole set, you can recursively divide to calculate the sum square deviation from the mean, and as with the mean calculation, divide by the total size and take square root at the end. [Edit: in fact all you need to calculate s.d is the sumsquare, the sum, and the count. Forgot about that. So you don’t have to calculate the mean first]