# Variance confusion

• July 30th 2007, 02:18 AM
psgame_freak
Variance confusion
Im confused with the formulas VAR[f(x)] = a^2VAR(X + b) and Sum of Independent Random VAR(C) = VAR(A) + VAR(B)

-Adult males of a certain species of animal are known to have a mean weight of 1.3 kg with standard error of .2 kg.

Q: What is the standard error of the total weight of randomly selected groups of 4 males?

Now I have 2 solutions with different answers.

Using VAR[f(x)] = a^2VAR(X + b)

= 4^2 (.2^2)
= 0.64 kg
hence Standard error is 0.8 kg

Using VAR(C) = VAR(A) + VAR(B)

= .2^2 + .2^2 + .2^2 + .2^2
= 0.16 kg
hence Standard error is 0.4 kg

Which one is right?
If its not much to ask, could you give me a link to help me with this?
How do we choose the constant?
• July 30th 2007, 03:40 AM
JakeD
Quote:

Originally Posted by psgame_freak
Im confused with the formulas VAR[f(x)] = a^2VAR(X + b) and Sum of Independent Random VAR(C) = VAR(A) + VAR(B)

-Adult males of a certain species of animal are known to have a mean weight of 1.3 kg with standard error of .2 kg.

Q: What is the standard error of the total weight of randomly selected groups of 4 males?

Now I have 2 solutions with different answers.

Using VAR[f(x)] = a^2VAR(X + b)

= 4^2 (.2^2)
= 0.64 kg
hence Standard error is 0.8 kg

Using VAR(C) = VAR(A) + VAR(B)

= .2^2 + .2^2 + .2^2 + .2^2
= 0.16 kg
hence Standard error is 0.4 kg

Which one is right?
If its not much to ask, could you give me a link to help me with this?
How do we choose the constant?

$Var(4X) = 4^2Var(X)$ applies to one variable.

$Var(X_1 + X_2 + X_3 + X_4) = Var(X_1) + Var(X_2) + Var(X_3) + Var(X_4)$ applies to 4 independent variables, which is the case here.