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Question
Calculate the quartile deviation and its coefficient from the following data:
| Age in Years: | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| No. of Members: | 13 | 61 | 47 | 15 | 10 | 18 | 36 |
Solution
| Age in Years (X) |
No. of Members (f) |
Cumulative Frequency (cf) |
| 20 | 13 | 13 |
| 30 | 61 | 74 |
| 40 | 47 | 121 |
| 50 | 15 | 136 |
| 60 | 10 | 146 |
| 70 | 18 | 164 |
| 80 | 36 | 200 |
| N = ∑f = 200 |
Q1 = Size of `(("N" + 1)/4)^"th"` value
= Size of `((200 + 1)/4)^"th"` value
= Size of `(201/4)^"th"` value
= Size of 50.25th value
Q1 = 30
Q3 = Size of `((3("N" + 1))/4)^"th"` value
= Size of `((3 xx 202)/4)^"th"` value
= Size of `(606/4)^"th"` value
= Size of 151.5th value
Q3 = 70
QD = `1/2 ("Q"_3 - "Q"_1)`
= `1/2 (70 - 30)`
= `1/2 xx 40`
QD = 20
Coefficient of QD = `("Q"_3 - "Q"_1)/("Q"_3 + "Q"_1)`
= `(70 - 30)/(70 + 30)`
= `40/100`
= 0.4
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