Q256 / 270 · NDA 2021 (Phase 1) · Mathematics

If $M$ is the mean of $n$ observations $x_1-k, x_2-k, x_3-k$, $\ldots, x_n-k$, where $k$ is any real number, then what is the mean of $x_1, x_2, x_3, \ldots, x_n$ ?

  • A
    $M$
  • Correct answer
    B
    $M+k$
  • C
    $M-k$
  • D
    $k M$

Solution

$M=\frac{\sum_{i=1}^n\left(x_i-k\right)}{n}$ $\begin{aligned}& M+K=\frac{\sum_{i=1}^n x_i}{n} \\& \therefore \quad \text { Mean }=M+K\end{aligned}$

Hence, the correct answer is option: 'B'.

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