Search any question & find its solution
Question:
Answered & Verified by Expert
The mean of set of $n$ numbers when each in divided by 5 is $\frac{X}{5}$, then mean of the $n$ number is
Options:
Solution:
2753 Upvotes
Verified Answer
The correct answer is:
$X$
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 $X$.
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 $X$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.