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Which of the following is the missing frequency of the given table if the median of the distribution is 24?

Class
0-10
10-20
20-30
30-40
40-50
Frequency
5
25
?
18
7

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answer is D.

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Detailed Solution

Consider the given frequency table,

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	25	?	18	7

The cumulative frequency table will be:

Class interval	Frequency	Cumulative frequency
0-10	5	5
10-20	25	$30 (f)$
20-30	$x (f)$	$30 + x$
30-40	18	$48 + x$
40-50	7	$55 + x$
	$N = 55 + x$

Given that, median = 24.
Therefore, the median class is 20-30
We know that,

Median = l + h × N 2 − c f f

, where

l =

lower limit of the median class,

h =

size of the median class,

f =

frequency of the median class,

N =

sum of frequencies and

c . f . =

cumulative frequency of the class just preceding the median class.
Then,

\frac{N}{2} = \frac{55 + x}{2}

l = 20 h = 10 c . f = 30 f = x

Substituting the values,

24 = 20 + \frac{\frac{55 + x}{2} - 30}{x} \times 10

24 - 20 = \frac{\frac{55 + x}{2} - 30}{x} \times 10

4 x = (\frac{55 + x}{2} - 30) \times 10

4 x = 275 + 5 x - 300

4 x - 5 x = 275 - 300

- x = - 25

x = 25

Hence, the missing frequency is 25.
Therefore, option 4 is correct.

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