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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`
= 94.5 + 4.85
= 99.35
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