Find out median of the series of the following table:\

Items 3 4 5 6 7 8

Frequency 6 9 11 14 23 10

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Solution

Items Frequency
(f) Cumulative Frequency
(c.f.)

3
4
5
6
7
8 6
9
11
14
23
10 6
15
26
40
63
73

N = 73

Median = size of ${(\frac{N + 1}{2})}^{t h}$ item
or, Median = size of ${(\frac{73 + 1}{2})}^{t h}$ item
or, Median = size of ${(\frac{74}{2})}^{t h}$ item = size of 37^th item.
Now, we need to locate this item in the column of Cumulative Frequency. The item just exceeding 37^th is 40 (in the c.f. column), which is corresponding to 6. Hence, median is 6.

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