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Question
The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
| Marks: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| Frequency: | 3 | 5 | 16 | 12 | 13 | 20 | 5 | 4 | 1 | 1 |
Solution
| Marks: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| Frequency: | 3 | 5 | 16 | 12 | 13 | 20 | 5 | 4 | 1 | 1 |
Here the maximum frequency is 20, then the corresponding class 50 – 60 is model class
L = 50, h = 60 – 50 = 10, f = 20, f1 = 13, f2 = 5
Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`
`=50+(20-13)/(40-13-5)xx2`
`=50+(7xx10)/22`
`=50+70/22`
= 50 + 3.18
= 53.18
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