The AM of n observations is M. If the sum of (n - 4) observations is a ,then the mean of remaining four observations is

A
$\frac{nM - a}{4}$
B
$\frac{nM + a}{2}$
C
$\frac{nM - a}{2}$
D
$nM + a$

Solution:

Let $x_{1}, x_{2}, \dots, x_{n}$ be n observations.

$\begin{array}{l} \begin{aligned} ∴ M & = \frac{x_{1} + x_{2} + x_{3} + \dots + x_{n}}{n} \\ = \frac{x_{1} + x_{2} + \dots + x_{n - 4} + x_{n - 3} + x_{n - 2} + x_{n - 1} + x}{n} \end{aligned} \\ \Rightarrow nM = a + x_{n - 3} + x_{n - 2} + x_{n - 1} + x_{n} \\ \Rightarrow \frac{nM - a}{4} = \frac{x_{n - 3} + x_{n - 2} + x_{n - 1} + x_{n}}{4} \end{array}$

Solution:

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