This has been bugging me for a while-

[sillymesaysme]

Linear combinations of variance-

Example question- If there are 4 men with a standard deviation in weight of 10 pounds, what is the variance of the 4 men together?

Which of the 2 methods is correct? And why is there the discrepancy if both methods seem to intuitively work?

a)
Var(4 men) = 10^2 + 10^2+ 10^2 + 10^2 = 4(10^2) = 400.

b)
Var(y=a+bx) = b^2*var(x)*2
var(4x) = 4^2(10^2) = 1600

I found examples of both from credible sources-
a) Example 4.1, b
http://web.as.uky.edu/statistics/users/viele/sta281f04/lintrans.pdf

b) Under "working with the Sums"
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/50250.html

Thanks!!!