Question

The mean of the given data is $30$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$8$	$10$	$f_1$	$15$	$f_2$

If total data is $70$, then missing numbers are

• A. $14$, $23$
• B. $25$, $21$
• C. $24$, $13$
• D. $40$, $31$

Answer 1

Answer: (A)

We have,

Class	$x$	$f$	$fx$
$0-10$	$5$	$8$	$40$
$10-20$	$15$	$10$	$150$
$20-30$	$25$	$f_1$	$25\,f_1$
$30-40$	$35$	$15$	$525$
$40-50$	$45$	$f_2$	$45\,f_2$

Also, $\Sigma f = 70$, $\Sigma f x = 25f_{1}+45f_{2}+715$
$\Rightarrow 8 + 10 + f_{1}+ 15 + f_{2} = 70$
$\Rightarrow f_{1}+f_{2} = 37\quad\ldots\left(i\right)$
and $\bar{x} = \frac{\Sigma fx}{\Sigma f}$
$\Rightarrow 5f_{1}+9f_{2} = 277\quad\ldots\left(ii\right)$
Solving $\left(i\right)$ and $\left(ii\right)$, we get $f_{1} = 14$ and $f_{2} = 23$