Q. If the mean of a set of observations $x_{1},x_{2},\ \ldots x_{10}$ is 20, then the mean of $x_{1} + 4,\ x_{2} + 8,\ \ldots x_{10} + 40$ is
A) 34
B) 38
C) 40
D) 42
Explanation
(d)
Mean $= \frac{1}{10}\lbrack\left( x_{1} + x_{2} + ... + x_{10} \right) + (4 + 8 + ... + 40)\rbrack$
$= \frac{1}{10}\left( x_{1} + x_{2} + \ldots + x_{10} \right) + \frac{4}{10}(1 + 2 + \ldots + 10)$
$= 20 + \frac{4 \times 10 \times 11}{10 \times 2} = 42$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.