# Standard deviation of series of trials

1. May 2, 2013

### Gauss M.D.

Say we want to saw ten planks and we have two methods available - one is sawing them all at once, ensuring they're all exactly uniform length. The other method is sawing them individually. Either method has EV of 1m and a standard deviation of 0.005m. I want to find the standard deviation of both methods.

In other words, given a random variable X, I guess what we're trying to figure out is SD(10X) and SD(X1 + X2 + ... + X10).

I'm not sure how to calculate the second one. Anyone want to give me a push? :S

2. May 2, 2013

### CompuChip

$$\operatorname{SD}(A + B + \cdots + Z) = \sqrt{\operatorname{SD}(A)^2 + \operatorname{SD}(B)^2 + \cdots + \operatorname{SD}(Z)^2}$$

What this basically says is that the variance Var(X) = SD(X)² is linear:
$$\operatorname{Var}(A + B + \cdots + Z) = \operatorname{Var}(A) + \operatorname{Var}(B) + \cdots + \operatorname{Var}(Z)$$

Also note that by setting A = B = ... = X you can actually derive the result for SD(10X).

3. May 2, 2013

### Gauss M.D.

Thanks a ton!