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प्रश्न
Find the Q.D. for the following data.
3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3.
उत्तर
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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