Question

There are 50 numbers Each numbers is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5 The mean of the given numbers is

• A. $48.9$
• B. $49.5$
• C. $52.5$
• D. $56.5$

Answer 1

The correct option is B $49.5$

$\Rightarrow$ Total observation is $50$

$\Rightarrow$ Let sum of $50$ number be $x$

$\therefore$ $\frac{x-(50\times 53)}{50}=-3.5$

$\therefore$ $x-2650=-3.5\times 50$

$\therefore$ $x-2650=-175$

$\therefore$ $x=-175+2650$

$\therefore$ $x=2475$

$\Rightarrow$ Original mean = $\frac{2475}{50}=49.5$