Tham KY's answer to Sin Wei Chuen's Junior College 2 H2 Maths Singapore question.
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Date Posted:
4 years ago
May I know why the 1/3 needs to be squared for variance? I recall Var(aX) = a^2 Var(X) but specifically for averages: X bar~N(μ, σ^2/n) not n^2?
All constant multipliers need to be squared when calculating variance. 1/3 means (1/3)*X too, the a in aX doesn't mean only for integer...
How is it then when we do sampling (when using CLT), we use σ^2/n not /n^2? and sum of independent observations as nσ^2 not n^2 σ^2? (pardon my confusion...)
See if the second photo explains your doubt...
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