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Question
Calculate Quartile deviation and Coefficient of Quartile deviation of the following data.
| Marks: | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| No. of students: | 150 | 142 | 130 | 120 | 72 | 30 | 12 | 4 |
Solution
| Marks (x) |
Frequency (f) |
Cumulative Frequency |
| 0 | 150 | 150 |
| 10 | 142 | 292 |
| 20 | 130 | 422 |
| 30 | 120 | 542 |
| 40 | 72 | 614 |
| 50 | 30 | 644 |
| 60 | 12 | 656 |
| 70 | 4 | 660 |
| N = 660 |
Q1 = Size of `(("N" + 1)/4)^"th"` value
= Size of `((660 + 1)/4)^"th"` value
= Size of (165.25)th value
Q1 = 10
Q3 = Size of `3(("N" + 1)/4)^"th"` value
= Size of 3(165.25)th value
= Size of (495.75)th value
Q3 = 30
Quartile deviation = `1/2 ("Q"_3 - "Q"_1)`
= `1/2 (30 - 10)`
= `20/2`
= 10
Co-efficient of Quartile deviation = `("Q"_3 - "Q"_1)/("Q"_3 + "Q"_1)`
= `(30 - 10)/(30 + 10)`
= `20/40`
= `1/2`
= 0.5
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