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. 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,
$\frac{x_{1}+4+x_{2}+8+x_{3}+12+...+x_{10}+40}{10}$
$=\frac{x_{1}+x_{2}+...+x_{10}}{10}+\frac{4(1+2+\ldots+10)}{10}$
$-20+\frac{4 \times 55}{10}-20+\frac{220}{10}$
$=20+ 22=42$