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Question
Calculate the median from the following data:
| Marks below: | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| No. of students: | 15 | 35 | 60 | 84 | 96 | 127 | 198 | 250 |
Solution
| Marks below | No of students | Class interval |
Frequency | Cumulative frequency |
| 10 | 15 | 0 - 10 | 15 | 15 |
| 20 | 35 | 10 - 20 | 20 | 35 |
| 30 | 60 | 20 - 30 | 25 | 60 |
| 40 | 84 | 30 - 40 | 24 | 84 |
| 50 | 96 | 40 - 50 | 12 | 96 |
| 60 | 127 | 50 - 60 | 37 | 127 |
| 70 | 198 | 60 - 70 | 71 | 198 |
| 80 | 250 | 70 - 80 | 52 | 250 |
| N = 250 |
Here, N = 250
So, N/2 = 125
Thus, the cumulative frequency just greater than 125 is 127 and the corresponding class is 50 - 60.
Therefore, 50 - 60 is the median class.
Here, l = 50, f = 31, F = 96 and h = 10
We know that
Median `=l+{(N/2-F)/f}xxh`
`=50+{(125-96)/31}xx10`
`=50+(29xx10)/31`
`=50+290/31`
= 50 + 9.35
= 59.35
Hence, the median is 59.35.
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