Question

The mean of 6 numbers is 42. If one number is excluded, the mean of remaining numbers is 45. Find the excluded number.

• A. 26
• B. 27
• C. 28
• D. 29

Answer 1

The correct option is B 27

We know,
$Mean$ = $\frac{Sumofobservations}{Numbersofobservations}$

Given that Mean = 42
and numbers of observations = 6
$\Rightarrow$ 42 = $\frac{Sumofobservations}{6}$
$\Rightarrow$ 42 X 6 = Sum of observations
$\Rightarrow$ Sum of 6 observations = 252

If one observation is excluded, the number of observations becomes 5 and mean is given as 45.
Let $x$ be a excluded number.
So, sum of observations will be 252 -$x$.

$Mean$ = $\frac{Sumofobservations}{Numbersofobservations}$
$45$ = $\frac{252-x}{5}$
$\Rightarrow$ $45\times 5$ = 252 -$x$
$\Rightarrow$ 225 = 252 -$x$
$\Rightarrow$ $x$ = 252 - 225
$\Rightarrow$ $x$ = 27
Thus, the excluded number is 27.