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प्रश्न
Calculate Q. D. for the following data:
| X | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| F | 6 | 5 | 3 | 2 | 4 | 7 | 3 |
उत्तर
| X | F | c.f. (less than type) |
| 24 | 6 | 6 |
| 25 | 5 | 11 ← Q1 |
| 26 | 3 | 14 |
| 27 | 2 | 16 |
| 28 | 4 | 20 |
| 29 | 7 |
27 ← Q3 |
| 30 | 3 | 30 |
| Total | 30 |
Here, N = 30
Q1 = value of `(("N" + 1)/4)^"th"` observation
= value of `((30 + 1)/4)^"th"` observation
= value of (7.75)th observation
Cumulative frequency which is just greater than (or equal to) 7.75 is 11.
∴ Q1 = 25
Q3 = value of `[3(("n" + 1)/4)]^"th"` observation
= value of `[3((30 + 1)/4)]^"th"` observation
= value of (3 × 7.75)th observation
= value of (23.25)th observation
Cumulative frequency which is just greater than (or equal to) 23.25 is 27.
∴ Q3 = 29
∴ Q.D. = `("Q"_3 - "Q"_1)/(2)`
= `(29 - 25)/(2)`
= `(4)/(2)`
∴ Q.D. = 2
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