Find the Q.D. for the following data.3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3. - Mathematics and Statistics

Sum

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

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 3^rd 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 9^th observation
∴ Q₃ = 16

Q.D. = `("Q"_3-"Q"_1)/(2)`

= `(16 - 5)/(2)`

= `(11)/(2)`
∴ Q.D. = 5.5

Concept: Measures of Dispersion - Quartile Deviation (Semi - Inter Quartile Range)

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Chapter 2 Measures of Dispersion
Exercise 2.1 | Q 4 | Page 26