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प्रश्न
Find the ‘mean’ and ‘mode’ of the following data:
| Class | 15 − 20 | 20 − 25 | 25 − 30 | 30 − 35 | 35 − 40 | 40 − 45 |
| Frequency | 12 | 10 | 15 | 11 | 7 | 5 |
योग
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उत्तर
| Class | Frequency (f) |
Mid-value (x) |
fx |
| 15 – 20 | 12 | 17.5 | 210.0 |
| 20 – 25 | 10 → f0 | 22.5 | 225 |
| 25 – 30 | 15 → f1 | 27.5 | 412.5 |
| 30 – 35 | 11 → f2 | 32.5 | 357.5 |
| 35 – 40 | 7 | 37.5 | 262.5 |
| 40 – 45 | 5 | 42.5 | 212.5 |
| Total | `bb(sumf = 60)` | `bb(sumfx = 1680.0)` |
Mean = `(sumfx)/(sumf)`
= `1680/60`
= 28
So, the mean of given data is 28.
Mode:
The class 25 – 30 has the highest frequency of 15.
f1 = 15, f0 = 10, f2 = 11
l = 25, h = 5
Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`
= `25 + ((15 - 10)/(2 xx 15 - 10 - 11)) xx 5`
= `25 + ((5))/(30 - 21) xx 5`
= `25 + 5/9 xx 5`
= `(225 + 25)/9`
= `250/9`
= 27.78
Therefore, the mode of the given data is 27.78.
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