I've been fooling around with some numbers while learning R and would like to know if the following is generalizable.
When I calculated the mean of numbers 1 through 100, I got this:
> mean(1:100)  50.5
Then when I calculated the mean of equal length subsets, I got the same:
> mean25 <- mean(1:25) > mean50 <- mean(26:50) > mean75 <- mean(51:75) > mean100 <- mean(76:100) > mean(c(mean25, mean50, mean75, mean100))  50.5
As an aside, when calculating the mean of different length subsets, the mean is expectedly not the same:
> mean5 <- mean(1:5) > mean37 <- mean(6:37) > mean91 <- mean(38:91) > mean100 <- mean(92:100) > mean(c(mean5, mean37, mean91, mean100))  46.25
Would it be accurate to say the mean of equal length subsets is always equal to the mean of the set? Are there any counterexamples to this?
Thanks in advance.