Question

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

• A. 34
• B. 32
• C. 42
• D. 38
• E. 40

Answer 1

Answer: (C)

Mean of a set of observations
$x_1,x_2,...,x_{10}=20$
Then, according to question,
$\frac{x_1+4+x_2+8+x_3+12+...+x_{10}+40}{10}$
$=\frac{x_1+x_2+...+x_{10}}{10}+\frac{4(1+2+\dots +10)}{10}$
$-20+\frac{4\times 55}{10}-20+\frac{220}{10}$
$=20+22=42$