Q74 / 160 · AP EAMCET 2021 (24 Aug Shift 1) · Mathematics

The mean of set of $n$ numbers when each in divided by 5 is $\frac{X}{5}$, then mean of the $n$ number is

  • A
    $5 X$
  • Correct answer
    B
    $X$
  • C
    $25 X$
  • D
    $\frac{x}{25}$

Solution

Mean of n number when each is divided by 5 is $\frac{x}{5}$. Let $x_1, x_2, x_3, \ldots, x_n$ are the number. $$ \therefore \text { Given mean }=\frac{\text { Sum of observation }}{\text { Total number of observation }} $$ $$ \begin{aligned} \frac{X}{5} & =\frac{\frac{x}{5}+\frac{x_2}{5}+\frac{x_3}{5}+\ldots+\frac{x_n}{5}}{n} \\ \frac{X}{5} & =\frac{1}{5} \frac{\left(x_1+x_2+x_3+. .+x_n\right)}{n} \\ X & =\frac{x_1+x_2+x_3+\ldots+x_n}{n} \end{aligned} $$ $\therefore$ Mean of $x_1, x_2, x_3, \ldots, x_n$ is $X$.

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

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