Find the median of the following frequency distribution:

Class 0-10 10-20 20-30 30-40 40-50

Frequency 2 12 22 8 6

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Solution

Class

Frequency $(f_{i})$

Cumulative frequency $(c . f)$

0-10

2

2

10-20

12

14

20-30

22

36

30-40

8

44

40-50

6

50

$N = 50 ∴ \frac{N}{2} = 25$
The cumulative frequency just greater than 25 is 36.

$∴ Median class = 20 - 30 i . e ., x_{k} = 20, h = 10, f = 22, c = c . f of the preceeding class = 14, \frac{N}{2} = 25 ∴ M_{e} = x_{k} + h \times \frac{\frac{N}{2} - c}{f} = 20 + (10 \times \frac{25 - 14}{22}) = 20 + 5 = 25$

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Similar questions

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	3	6	8	15	10	8

Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	4	4	8	10	12	8	4

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	10	20	5	10

Class	less than 10	10−20	20−30	30−40	40−50	50−60	more than 60
Frequency	5	12	18	22	6	4	3

Find the median of the following data:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	Total
Frequency	$8$	$16$	$36$	$34$	$6$	$100$

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