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Following is the Distribution of I.Q. of Loo Students. Find the Median I.Q. - CBSE Class 10 - Mathematics

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Question

Following is the distribution of I.Q. of loo students. Find the median I.Q.

I.Q.: 55 - 64 65 - 74 75 - 84 85 - 94 95 - 104 105 - 114 115 - 124 125 - 134 135 - 144
No of Students: 1 2 9 22 33 22 8 2 1

Solution

Class interval(inclusive) Class interval(exclusive) Frequency Cumulative frequency(c.f)
55 - 64 54.5 - 64.5 1 1
65 - 74 64.5 - 74.5 2 3
75 - 84 74.5 - 84.5 9 12
85 - 94 84.5 - 94.5 22 34
95 - 104 94.5 - 104.5 33 67
105 - 114 104.5 - 114.5 22 89
115 - 124 114.5 - 124.5 8 97
125 - 134 124.5 - 134.5 2 99
135 - 144 134.5 - 144.5 1 100
    N = 100  

Here, N = 100

So, N/2 = 50

Thus, the cumulative frequency just greater than 50 is 67 and the corresponding class is 94.5−104.5.

Therefore, 94.5−104.5 is the median class.

Here, l = 94.5, f = 33, F = 34 and h = 10

We know that,

Median `=l+{(N/2-F)/f}xxh`

`=94.5+((50-34)/33)xx10`

`=94.5+160/33`

94.4.85

99.35

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Solution Following is the Distribution of I.Q. of Loo Students. Find the Median I.Q. Concept: Median of Grouped Data.
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