Question

There are $5$ numbers such that their mean is equal to their median. If $4$ of the numbers are $14,8,16$ and $14$, what is the $5^{th}$ number?

• A. $13$
• B. $14$
• C. $15$
• D. $16$
• E. $18$

Answer 1

The correct option is E $18$

$\Rightarrow$ The given numbers are $8,14,14,16$

$\Rightarrow$ The Median is the middle number

$\Rightarrow$ We now know that the median is $14$ and the mean is equal to the median

$\therefore$ The mean $=14$

$\Rightarrow$ The mean is the total of the $5$ numbers divided by $5$

$\therefore$ The total of the $5$ numbers $=14\times 5=70$

$\Rightarrow$ The existing numbers $=8+14+14+16=52$

$\therefore$ The $5th$ number that is missing $=70-52=18$