Question

Compute all the quartiles for the following series of observations:
16, 14.9, 11.5, 11.8, 11.1, 14.5, 14, 12, 10.9, 10.7, 10.6, 10.5, 13.5, 13, 12.6.

Answer 1

The given data can be arranged in ascending order as follows:
10.5, 10.6, 10.7, 10.9, 11.1, 11.5, 11.8, 12, 12.6, 13, 13.5, 14, 14.5, 14.9, 16
Here, n = 15

Q₁ = value of `(("n" + 1)/4)^"th"`observation

= value of `((15 + 1)/4)^"th"`observation

= value of 4^th observation
∴ Q₁ = 10.9
Q₂ = value of `2(("n" + 1)/4)^"th"`observation

= value of `2((15 + 1)/4)^"th"`observation

= value of (2 × 4)^th observation

= value of 8^th observation
∴ Q₂ = 12

Q₃ = value of `3(("n" + 1)/4)^"th"`observation

= value of `3((15 + 1)/4)^"th"`observation

= value of (3 × 4)^th observation

= value of 12^th observation
∴ Q₃ = 14