Question

If the mean of a set of observations $x_1,x_2,.......,x_{10}$ is 20, then the mean of $x_1+4,x_2+8,x_3+12,...,x_{10}+40$ is

• A. 34
• B. 42
• C. 38
• D. 40

Answer 1

Answer: (B)

42

Here, $\frac{x_1+x_2+x_3+.............+x_{10}}{10}=20$
$\Rightarrow x_1+x_2+x_3+........+x_{10}=200..\left(1\right)$
Thus New mean $=\frac{x_1+4+x_2+8+x_3+12+.............+x_{10}+40}{10}$
$=\frac{(x_1+x_2+x_3+......+x_{10})+(4+8+12+16+........+40)}{10}$
$=\frac{200+\frac{10}{2}(4+40)}{10}=\frac{420}{10}=42$