The mean of the following is $52$ and the frequency interval $30 - 40$ is $^{'} f$ . Find the value of .
Class interval 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
Frequency 5 3 f 7 2 6 13

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Solution

Mean $= \frac{\sum f x}{\sum f} = \frac{1940 + 35 f}{36 + f}$ …… (i)

But, given mean $= 52$ …. (ii)

From (i) and (ii), we have

$\frac{1940 + 35 f}{36 + f} = 52$

$1940 + 35 f = 1872 + 52 f$

$17 f = 68$

Thus, $f = 4$

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Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	45	75	35	25	15

Class-interval:	25−30	30−35	35−40	40−45	45−50	50−55
Frequency:	25	34	50	42	38	14

Class:	0−10	10−20	20−30	30−40	40−50	50−60	60–70
Frequency:	8	10	10	16	12	6	7

46

p

q

class interval	10-20	20-30	30-40	40-50	50-60	60-70	70-80	Total
Frequency	12	30	p	65	q	25	18	230

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

Class-interval:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency:	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

Class-interval:	10-15	15-20	20-25	25-30	30-35	35-40
Frequency:	$30$	$45$	$75$	$35$	$25$	$15$

Class-interval:	25-30	30-35	35-40	40-45	45-50	50-60
Frequency:	$25$	$34$	$50$	$42$	$38$	$14$

\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 10 - 20 & 5 20 - 30 & 3 30 - 40 & f 40 - 50 & 7 50 - 60 & 2 60 - 70 & 6 70 - 80 & 13 \end{matrix}

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Class interval	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	5	3	f	7	2	6	13