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प्रश्न
Find the mode of the given data:
| Class Interval | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 |
| Frequency | 15 | 6 | 18 | 10 |
उत्तर
Here the maximum class frequency is 18, and the class corresponding to this frequency is 40-60.
So, the modal class is 40-60.
Now,
Modal class = 40-60, lower limit (/) of modal class – 40, class size (h)=20,
Frequency `(f_1)` of the modal class =18,
Frequency (𝑓0) of class preceding the modal class =6,
Frequency (𝑓2) of class succeeding the modal class = 10.
Now, let us substitute these values in the formula:
𝑀𝑜𝑑𝑒=𝑙+`((f_1−f_0)/(2f_1−f_0−f_2)) ×ℎ`
`= 40+((18−6)/(36−6−10)) ×20`
`= 40+(12/20) ×20`
= 40+12
= 52
Hence, the mode is 52.
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