Calculate median from following data:

X Below 10 10−20 20−30 30−40 40−50 50 and Above

Frequency 3 7 15 9 6 4

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Solution

X Frequency
(f) Cumulative Frequency
(c.f.)

0 − 10
10 − 20 3
7 3
10 (c.f.)

20 − 30 15 (f) 25

30 − 40
40 − 50
50 − 60 9
6
4 34
40
44

$N = \sum_{}^{} f = 44$

Median class is given by the size of ${(\frac{N}{2})}^{th}$ item, i.e. ${(\frac{44}{2})}^{th}$ item, which is 22^nd item.
This corresponds to the class interval of (20 − 30), so this is the median class.
$Median = l_{1} + \frac{\frac{N}{2} - c . f .}{f} \times i so, Median = 20 + \frac{\frac{44}{2} - c . f .}{f} \times i or, Median = 20 + \frac{22 - 10}{15} \times 10 or, Median = 20 + 8 = 28 Thus, Median = 28$

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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
No of students	3	?	15	9	?	4

Class Interval	0-10	10-20	20-30	30-40	40-50	50-70
Frequency	7	10	8	20	32	28

X	Below 10	10−20	20−30	30−40	40−50	50 and Above
Frequency	3	7	15	9	6	4

Size	0−10	10−20	20−30	30−40	40−50	50−60
Frequency	3	10	20	7	6	4

Variable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	35	40	25	25	15