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Question

Find the missing frequency form the following distribution, if median is 35 and N = 170.
Variables 0−10 10−20 20−30 30−40 40−50 50−60 60−70
Frequency 10 20 ? 40 ? 25 15

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Solution

Given, Median = 35
N=170
Let the missing frequencies be f1 & f2.
Class Interval Frequency
(f)
Cumulative Frequency
0 − 10
10 − 20
20 − 30
10
20
f1
10
30
30 + f1 (c.f.)
30 − 40 40 (f) 70 + f1
40 − 50
50 − 60
60 − 70
f2
25
15
70 + f1 + f2
95 + f1 + f2
110 + f1 + f2
N = ∑f =170


Median class is given by the size of N2th item, i.e.1702th item, which is 85th item.
This corresponds to the class interval of (30 40) as median is 35.
Median=l1+N2-c.f.f×iso, 35=30+1702-(30+f1)40×10or, 35=30+85-30-f140×10or, 20=55-f1or, f1= 35 f1 = 35


110 + f1 + f2 = 170
or, f2 = 170 − 110 − 35
f2 = 25

Therefore, f1 is 35 and f2 is 25.

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