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?

Quote:

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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?

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applies to one variable.

applies to 4 independent variables, which is the case here.

The second answer is correct.

Searching on "variance sum independent variables" turns up links with explanations, but I didn't see one that really stood out. How about Variance - Wikipedia, the free encyclopedia?