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Question
Find the Q.D. for the following data.
3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3.
Solution
The given data can be arranged in ascending order as follows:
3, 3, 5, 5, 8, 9, 11, 15, 16, 17, 19.
Here, n = 11
Q1 = value of `(("n"+1)/4)^"th"` observation
= value of `((11+1)/4)^"th"` observation
= value of 3rd observation
∴ Q1 = 5
Q3 = value of `3(("n"+1)/4)^"th"` observation
= value of `3((11 + 1)/4)^"th"` observation
= value of (3 × 3)th observation
= value of 9th observation
∴ Q3 = 16
Q.D. = `("Q"_3-"Q"_1)/(2)`
= `(16 - 5)/(2)`
= `(11)/(2)`
∴ Q.D. = 5.5
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