Question

The standard deviation of a group of numbers is 10. If each number is multiplied by 2 and then 1 is subtracted , what is the new standard deviation ?

• A. 10
• B. -10
• C. 20
• D. 19

Answer 1

Answer:

C. 20

$\sigma=10$

$2x_i-1$

$\sigma^2=100$

$mean=\frac{(Σ2x_i-1)}{n}$

$=2\frac{1}{n}Σx_i-\frac{n}{n}$

=$2x-2$

$\frac{1}{n}Σ(x_i-x)^2=100$

$\frac{1}{n}Σ[(2x_i-1)-(2x-1)^2]$

$=\frac{1}{n}Σ(2x_i-1-2x+1)2$

$=4\frac{1}{n}Σ(x_i-x)^2=4\times100=400$

$SD=\sqrt{400}=20$