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Question
Find the mode of the following data:
| Marks | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 |
| Number of students | 22 | 38 | 46 | 34 | 20 |
Solution
| Marks | No. of students |
| 0 − 10 | 22 |
| 10 − 20 | 38 |
| 20 − 30 | 46 |
| 30 − 40 | 34 |
| 40 − 50 | 20 |
The highest frequency is 46
20 – 30 is the modal class
Here l = 20, f = 46, f1 = 38, f2 = 34 and c = 10
Mode = `("l" + (f - f_1))/((2f - f_1 - f_2)) xx "c"`
= `20 + ((46 - 38) xx 10)/((92 - 38 - 34))`
= `20 + (8 xx 10)/20`
= `20 + (8 xx 10)/20`
= 20 + 4
= 24
∴ Mode = 24
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