Question

The mean of a set of $5$ numbers is $90$. If one of the numbers is removed, the mean of the remaining numbers is $92$. Identify the removed number.

• A. $82$
• B. $84$
• C. $87$
• D. $90$
• E. $92$

Answer 1

The correct option is A $82$

Let the $5$ values be $a,b,c,d,e$ and the removed value is $e$.

Given that mean of $5$ values is $90$.

So, $\frac{a+b+c+d+e}{5}=90$

$\Rightarrow a+b+c+d+e=90\times 5=450$

If $e$ is removed, then mean of rest of the values is $92$

$\Rightarrow \frac{a+b+c+d}{4}=92$

$\Rightarrow a+b+c+d=368$

From both the equations, we get

$(a+b+c+d+e)-(a+b+c+d)=450-368$

$e=82$ is the removed number.