Question

The mean of the following distribution is $50$.

$x$	$10$	$30$	$50$	$70$	$90$
$f$	$17$	$5a+3$	$32$	$7a-11$	$19$

Find the value of $a$.

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (C)

$5$

Means is given as $50$

$\Rightarrow \frac{\sum _1^{5}xf}{\sum _1^{5}f}=50$

$\Rightarrow \frac{170+150a+90+1600+490a-770+1710}{17+5a+3+32+7a-11+19}=50$

$\Rightarrow 640a+2800=3000+600a$

$\Rightarrow 40a=200$

$\Rightarrow a=5$

Hence, option C.