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If the median of the following frequency distribution is 32.5,

Question

If the median of the following frequency distribution is $32.5$ , find the values of $f 1$ and $f 2$ .
Class interval $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ Total
Frequency $f_{1}$ $5$ $9$ $12$ $f_{2}$ $3$ $2$ $40$

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Sebastian Discussed

If the median of the following frequency distribution is

32.5

, find the values of

f 1

and

f 2

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	Total
Frequency	$f_{1}$	$5$	$9$	$12$	$f_{2}$	$3$	$2$	$40$

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Text solutionVerified

Sum of all the frequencies

= f 1 + 5 + 9 + 12 + f 2 + 3 + 2 = 40

(given)

\Rightarrow f 1 + f 2 = 9.... (1)

Median is

32.5

lies in

30 - 40

, so the median class is

30 - 40

N = 40

\frac{N}{2} = 20

I = 30, h = 10, f = 12

c f = f_{1} + 5 + 9 = f_{1} + 14

We know,
Median

= 1 + ⎩ ⎨ ⎧ h \times \frac{( \frac{N}{2} - c f )}{f} ⎭ ⎬ ⎫

Substitute all the values in the above formula, we get

32.5 = 30 + {10 \times \frac{( 20 - f _{1} - 14 )}{12}}

\Rightarrow 32.5 = 30 + \frac{( 30 - 5 f _{1} )}{6}

\Rightarrow 2.5 = \frac{( 30 - 5 f _{1} )}{6}

f_{1} = 3

From

(1)

\Rightarrow 3 + f_{2} = 9

\Rightarrow f_{2} = 6

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Question Text	If the median of the following frequency distribution is $32.5$ , find the values of $f 1$ and $f 2$ .
Answer Type	Text solution:1
Upvotes	150