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Question
Find the mode of the following distribution:
| Weight (in kgs) | 25 − 34 | 35 − 44 | 45 − 54 | 55 − 64 | 65 − 74 | 75 − 84 |
| Number of students | 4 | 8 | 10 | 14 | 8 | 6 |
Solution
In the given table the class intervals are in inclusive form; convert them into exclusive form.
| Class | Mid value (x) |
frequency (f) |
fx | cf |
| 24.5 − 34.5 | 29.5 | 4 | 118 | 4 |
| 34.5 − 44.5 | 39.5 | 8 | 316 | 12 |
| 44.5 − 54.5 | 49.5 | 10 | 495 | 22 |
| 54.5 − 64.5 | 59.5 | 14 | 833 | 36 |
| 64.5 − 74.5 | 69.5 | 8 | 556 | 44 |
| 74.5 − 84.5 | 79.5 | 6 | 477 | 50 |
| `sumf` = 50 | `sumfx` = 2975 |
The highest frequency is 14
Modal class is 54.5 – 64.5
Here l = 54.5, f = 14, f1 = 10, f2 = 8 and c = 10
mode = `"l" + ((f - f_1)/(2f - f_1 - f_2)) xx "c"`
= `54.5 + ((14 - 10))/((28 - 10 - 8)) xx 10`
= `54.5 + (4 xx 10)/10`
= 58.5
∴ Mode = 58.5
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