The median of the following distribution is 30. Find the missing frequencies f1 and f2:

Class frequency

0-10 10

10-20 10

20-30 f1

30-40 30

40-50 f2

50-60 10

Total 100

Question

The median of the following distribution is 30 Find the missing
frequencies f1 and f2:
Class frequency
0-10 10
10-20 10
20-30 f1
30-40 30
40-50 f2
50-60 10
Total 100

Ajanta Trivedi · Accepted Answer

class interval	frequency	cumulative frequency
0-10	10	10
10-20	10	20
20-30	$f_{1}$	$20 + f_{1}$
30-40	30	$50 + f_{1}$
40-50	$f_{2}$	$50 + f_{1} + f_{2}$
50-60	10	$60 + f_{1} + f_{2}$
total	100

therefore

$60 + f_{1} + f_{2} = 100 f_{1} + f_{2} = 100 - 60 f_{1} + f_{2} = 40.................. (1)$

given: median = 30

$\frac{n}{2} = \frac{100}{2} = 50$

therefore modal class = 30-40

$m e d i a n = l + \frac{h}{f} (\frac{n}{2} - c) 30 = 30 + \frac{10}{30} (50 - 20 - f_{1}) \frac{1}{3} (30 - f_{1}) = 0 30 - f_{1} = 0 \Rightarrow f_{1} = 30$

from eq(1):

$f_{2} = 40 - f_{1} f_{2} = 40 - 30 f_{2} = 10$

thus missing frequencies $f_{1} = 30 a n d f_{2} = 10$

hope this helps you.

cheers!!

The median of the following distribution is 30. Find the missing frequencies f1 and f2: Class frequency 0-10 10 10-20 10 20-30 f1 30-40 30 40-50 f2 50-60 10 Total 100

The median of the following distribution is 30. Find the missing frequencies f1 and f2:

Class frequency

0-10 10

10-20 10

20-30 f1

30-40 30

40-50 f2

50-60 10

Total 100