Find the mode from the following data.
| Class Interval | Frequency |
| 0 – 5 | 2 |
| 5 – 10 | 6 |
| 10 – 15 | 10 |
| 15 – 20 | 16 |
| 20 – 25 | 22 |
| 25 – 30 | 11 |
| 30 – 35 | 8 |
| 35 – 40 | 5 |
WBBSE
Class X
Mathematics
Statistics
04 Mark
2024
The class with the highest frequency is 20 – 25, so it is the modal class.
Let
- l = lower limit of modal class = 20
- h = class width = 5
- f₀ = frequency of the class before the modal class = 16
- f₁ = frequency of the modal class = 22
- f₂ = frequency of the class after the modal class = 11
Formula: Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
Mode = 20 + 22 − 16 \over 2 × 22 − 16 − 11 × 5
= 20 + 6 \over 44 − 27 × 5
= 20 + 6 \over 17 × 5
= 20 + 30 \over 17
= 20 + 1.76
= 21.76
Therefore, the mode is 21.76.
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