Find the missing frequency in the following distribution if $N = 100$ and median is $32$

Marks

0-10

10-20

20-30

30-40

40-50

50-60

Total

No. of students

10

?

25

30

?

10

100

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Solution

class f cf
0-10 10 10
10-20 x 10+x
20-30 25 35+x
30-40 30 65+x
40-50 y 65+x+y
50-60 10 75+x+y
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 75 + x + y$

$75 + x + y = 100$
$x + y = 25$

$f = 30, h = 10, c f = 35 + x, \frac{n}{2} = 50$

Median $= l + (\frac{\frac{n}{2} - c f}{f}) \times h$

$32 = (\frac{50 - 35 - x}{30}) \times 10$

$32 - 30 = \frac{15 - x}{3}$

$6 = 15 - x$

$x = 9$

$∴ y = 16$

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Similar questions

Marks obtained	0−10	10−20	20−30	30−40	40−50	50−60	Total
No. of Students	10	?	25	30	?	10	100

f_{1}

f_{2}

N = 100

32

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$T o t a l$
Frequency	$10$	$f_{1}$	$25$	$30$	$f_{2}$	$10$	$100$

100

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$10$	$15$	$25$	$50$

Marks	0−10	10−20	20−30	30−40	40−50
No. of Students	8	?	40	?	10

Variables	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	?	40	?	25	15

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Marks	0-10	10-20	20-30	30-40	40-50	50-60	Total
No. of students	10	?	25	30	?	10	100