Sample standard deviation proof

[autre]

Homework Statement

Let x_{1},...,x_{n} be n observations. If y_{1},...,y_{n} is another set of observations s.t. y_{i}=ax_{i}+b , prove that s_{y}=|a|s_{x} .

The Attempt at a Solution

Attempt at a proof: Since \bar{y}=a\bar{x} +b then \bar{x}=(\bar{y}-b)/a and s_{x}=\sqrt{\frac{1}{n-1}\sum(x_{i}-\frac{\bar{y}-b}{a})}. This is where I get stuck. Any ideas?

 

[Slats18]

First of all, you should know that standard deviation is independent of translation (change of origin), but is affected by scale. See if you can knock out the proofs of each separately, and then you should be able to put them together. Also, begin your proofs by using the variance, not the standard deviation.

 

[lanedance]

and it will probably be easier to calculate s_y directly and compare with the form of s_x