Question

The mean and median of the numbers 1, 2, 3, 4, y, 8, 9, 10, 12 and x written in increasing order are both 10, then the values of x and y are:

• A. $x=15,y=36$
• B. $x=39,y=12$
• C. $x=15,y=36$
• D. $x=39,y=15$

Answer 1

The correct option is B

$x=39,y=12$

Given numbers are 1, 2, 3, 4, y, 8, 9, 10, 12 and x
$\because \text{Mean}=\frac{\sum x_i}{N}\Rightarrow 10=\frac{1+2+3+4+y+8+9+10+12+x}{10}\Rightarrow 100=49+x+y\Rightarrow x+y=51$
$\text{and median}=\frac{\left(\frac{n}{2}\right)th\text{observation}+(\frac{n}{2}+1)th\text{observation}}{2}\Rightarrow 10=\frac{y+8}{2}\Rightarrow 20=y+8\Rightarrow y=12\therefore x=51-12$
$=39$