Question

The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be

• A. 40
• B. 45
• C. $40+\frac{21}{25}$
• D. none of these

Answer 1

The correct option is A

40

Let the numbers be $x_i.$ Then,
$\overline{x}=\frac{\sum x_i}{25}$
Let $y_i=x_i+5.$ Then,
$\overline{y}=\frac{\sum (x_i+5)}{25}=\overline{x}+5\Rightarrow (y_i-\overline{y})=(x_i+5)-(\overline{x}+5)=x_i-\overline{x}\Rightarrow \sigma \left(y\right)=\sqrt{\frac{(y_i-\overline{y}{)}^2}{n}}=\sqrt{\frac{(x_i-\overline{x}{)}^2}{n}}=\sigma \left(x\right)$