Question

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

Answer 1

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