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Calculate the missing frequency from the following distributio

Question

Calculate the missing frequency from the following distribution, it being given that 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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Calculate the missing frequency from the following distribution, it being given that 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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Text solutionVerified

Median

= 24

Median class

= 20 - 30

Here,

l = 20, h = 10, f = x, c f = 30, \frac{N}{2} = \frac{55 + x}{2}

\Rightarrow

M e d ian = l + \frac{\frac{N}{2} - c f}{f} \times h

\Rightarrow

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

\Rightarrow

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

\Rightarrow

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

\Rightarrow

4 x \times 2 = (55 + x - 60) \times 10

\Rightarrow

8 x = 550 + 10 x - 600

\Rightarrow

10 x - 8 x = 600 - 550

\Rightarrow

2 x = 50

∴

x = 25

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Question Text	Calculate the missing frequency from the following distribution, it being given that the median of the distribution is $24$ .
Answer Type	Text solution:1
Upvotes	150