Question

The mean of the following frequency distribution is $16.6$

$x_i$	$8$	$12$	$15$	$18$	$20$	$25$	$30$	Total
$f_i$	$12$	$16$	$p$	$24$	$16$	$q$	$4$	$100$

• A. $p=20$
• B. $q=8$
• C. $p=8$
• D. $q=20$

Answer 1

Answer: (A), (B)

The correct options are
A $q=8$
B $p=20$

We prepare the table as above.
Here, $\sum f_i=72+p+q$.
But, $\sum f_i=100$ (given).
$\therefore$ $72+p+q=100$
$p+q=28$
Also, mean = $\frac{\sum f_i{x}_i}{\sum f_i}$
$=\frac{1160+15p+25q}{72+p+q}$
$=\frac{1160+15(p+q)+10q}{72+(p+q)}$
$=\frac{1160+15\times 28+10q}{72+28}=\frac{1580+10q}{100}$
But mean = $16.6$ (given)
$\therefore$ $\frac{1580+10q}{100}=16.6$
$1580+10q=1660$
$10q=80$
$q=8$
$p+q=28$
$p=28-q=28-8=20$
Hence, $p=20$ and $q=8$