Find out the median of the following frequency distribution:

Marks 50 55 60 65 70 75

No. of Students 5 7 6 10 5 8

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Solution

Marks
Number of Students
(f) Cumulative Frequency (c.f.)

50
55
60
65
70
75 5
7
6
10
5
8 5
12
18
28
33
41

N= 41

Median = size of ${(\frac{N + 1}{2})}^{th}$ item
or, Median $= \frac{41 + 1}{2} = 21^{st} item$
Now, we need to locate this item in the column of Cumulative Frequency. The item exceeding 21^st is 28 (in the c.f. column), which is corresponding to 65. Hence, median is 65.

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Class Interval	40−45	45−50	50−55	55−60	60−65	65−70	70−75	75−80	80−85
Frequency	4	6	8	10	7	6	5	3	1

Weight (in kg)	40-45	45-50	50-55	55-60	60-65	65-70	70-75
Number of students	2	3	8	6	6	3	2

Find the mean of the following using step deviation method.

Marks	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60	60−65	65−70
Students	6	3	7	4	6	4	2	8	3	7

Calculate the mean for the following frequency distribution:

Marks	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	3	7	10	6	8	2	4

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