The arithmetic mean of the following frequency distribution is $53$ .find the value of $p$ .
Class $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$
frequency $12$ $15$ $32$ $p$ $13$

Open in App

Solution

Calculate the value of $\sum f_{i} x_{i}$ ,
Class Interval
Frequency
$(f i)$
Class mark $(x i)$ $= \frac{u p p e r c l a s s l i m i t + l o w e r c l a s s l i m i t}{2}$ $(x i f i)$
$0 - 20$ $12$ $10$ $120$
$20 - 40$ $15$ $30$ $450$
$40 - 60$ $32$ $50$ $1600$
$60 - 80$ $p$ $70$ $70 p$
$80 - 100$ $13$ $90$ $1170$
Total $\sum f_{i} = 72 + p$ $\sum f_{i} x_{i} = 3340 + 70 p$
Now,
$\bar{x} = \frac{\sum f i x i}{\sum f i}$
$\Rightarrow 53 = \frac{1900 + 70 p}{72 + p}$
$\Rightarrow 53 (72 + p) = 3340 + 70 p \Rightarrow 3816 + 53 p = 3340 + 70 p \Rightarrow 53 p - 70 p = 3340 - 3816 \Rightarrow - 17 p = - 476 \Rightarrow p = 28$

Hence, we get the value of $p = 28$ .

Suggest Corrections

Similar questions

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	12	15	32	x	13

54

p

Class:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency:	$7$	$p$	$10$	$9$	$13$

The arithmetic mean of the following frequency distribution is $47$ . Determine the value of $p$ .

Class-interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$8$	$15$	$20$	$p$	$5$

53

p

$C l a s s$	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
$F r e q u e n c y$	$15$	$18$	$21$	$p$	$17$

Join BYJU'S Learning Program

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
frequency	$12$	$15$	$32$	$p$	$13$

Class Interval	Frequency $(f i)$	Class mark $(x i)$ $= \frac{u p p e r c l a s s l i m i t + l o w e r c l a s s l i m i t}{2}$	$(x i f i)$
$0 - 20$	$12$	$10$	$120$
$20 - 40$	$15$	$30$	$450$
$40 - 60$	$32$	$50$	$1600$
$60 - 80$	$p$	$70$	$70 p$
$80 - 100$	$13$	$90$	$1170$
Total	$\sum f_{i} = 72 + p$		$\sum f_{i} x_{i} = 3340 + 70 p$