Find out median of the following series:

Size 15 20 25 30 35 40

Frequency 10 15 25 5 5 20

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Solution

Size Frequency
(f) Cumulative Frequency
(c.f.)

15
20
25
30
35
40 10
15
25
5
5
20 10
25
50
55
60
80

N = 80

Median = size of ${(\frac{N + 1}{2})}^{t h}$ item
or, Median = size of ${(\frac{80 + 1}{2})}^{t h}$ item
or, Median = size of 40.5^th item
Now, we need to locate this item in the column of Cumulative Frequency. The item just exceeding 40.5^th is 50 (in the c.f. column), which is corresponding to 25.
Hence, median is 25.

Suggest Corrections

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

Wage Rate (₹)	25−30	20−25	15−20	10−15	5−10	0−5
Number of Workers	5	10	20	5	8	2

Class-Interval	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	5	7	15	18	16	9	6	3

Class Interval	0−5	5−10	10−15	15−20	20−25	25−30
Frequency	20	24	32	28	20	26

Class	5-10	10-15	15-20	20-25	20-30	30-35	35-40	40-45
Frequency	5	6	15	10	5	4	2	2