Question

If standard deviation of variate $x_i$ is 10, then variance of the variate $(50+5x)$ will be

• A. 50
• B. 250
• C. 500
• D. 2500

Answer 1

The correct option is D 2500

We know, $Var(aX+b)=a^2.Var\left(x\right)$

Here $a=5,b=50$

$\therefore$ Required variance

$=Var(5x+50)=5^2.Var\left(x\right)=25\times {\sigma }^2=25\times {10}^2=2500$