Q. The AM of $n$ observations is$M$. If the sum of $(n - 4)$ observations is $a$, then the mean of remains four observations is
A) $\frac{nM - a}{4}$
B) $\frac{nM + a}{2}$
C) $\frac{nM - a}{2}$
D) $nM + a$
Explanation
(a)
Let $x_{1},x_{2},\ \ldots,x_{n}$ be $n$ observations
$\therefore\ \ M = \frac{x_{1} + x_{2} + x_{3} + ... + x_{n}}{n}$
$= \frac{x_{1} + x_{2} + ... + x_{n - 4} + x_{n - 3} + x_{n - 2} + x_{n - 1} + x_{n}}{n}$
$\Rightarrow \ \ nM = a + x_{n - 3} + x_{n - 2} + x_{n - 1} + x_{n}$
$\Rightarrow \ \frac{nM - a}{4} = \frac{x_{n - 3} + x_{n - 2} + x_{n - 1} + x_{n}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.