Question

The numbers $3,5,7$ and $9$ have their respective frequencies $x-2,x+2,x-3$ and $x+3$. If the arithmetic mean is $6.5$, then the value of $x$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (C)

$5$

Mean $=6.5=\frac{3\times (x-2)+5\times (x+2)+7\times (x-3)+9\times (x+3)}{x-2+x+2+x-3+x+3}$
$\therefore$ $6.5=\frac{3x-6+5x+10+7x-21+9x+27}{4x}$
$\therefore$ $6.5\times 4x=24x+10$
$\therefore$ $26x-24x=10$
$\therefore$ $x=5$