Find out median of the following series:

Size 20 25 30 35 40 45 50 55

Frequency 14 18 33 30 20 15 13 7

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Solution

Size Frequency Cumulative Frequency

20
25
30 14
18
33 14
14 + 18 = 32
32 + 33 = 65

35 30 65 + 30 = 95

40
45
50
55 20
15
13
7 95 + 20 = 115
115 + 15=130
130 + 13=143
143 + 7 = 150

N = 150

Median or M = Size of ${(\frac{N + 1}{2})}^{th}$ item
or, M = Size of ${(\frac{15 + 1}{2})}^{th}$ item
or, M = Size of 75.5^th item

It shows that median value corresponds to the 75.5th item in the series. This item appears first of all in 95^th cumulative frequency of the series. Therefore, median shall be the value corresponding to the 95^th cumulative frequency, which is 35.

Therefore, the median value will be 35.

Suggest Corrections

Age (Years)	55−60	50−55	45−50	40−45	35−40	30−35	25−30	20−25
Number of Students	7	13	10	15	30	33	28	14

Items	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Frequency	5	10	16	18	12	10	8

Size	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	5	7	13	21	16	8	3

Valuable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	7	12	18	25	16	14	8