Question

The heights (in cm) of 10 students are given below: 148, 171, 158, 151, 154, 159, 152, 163, 171, 145. Calculate Q₁ and Q₃ for above data.

Answer 1

The given data can be arranged in ascending order as follows:

145, 148, 151, 152, 154, 158, 159, 163, 171, 171.
Here, n = 10

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

= value of `((10 + 1)/4)^"th"`observation

= value of (2.75)^th observation
= value of 2^nd observation + 0.75 (value of 3^rd observation – value of 2^nd observation)
= 148 + 0.75 (151 – 148)
= 148 + 0.75 (3)
= 148 + 2.25
∴ Q₁ = 150.25

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

= value of `3((10 + 1)/4)^"th"`observation
= value of (3 × 2.75)^th observation
= value of (8.25)^th observation
= value of 8^th observation + 0.25 (value of 9^th observation –  value of 8^th observation)
= 163 + 0.25 (171 – 163)
= 163 + 0.25 (8)
= 163 + 2
∴ Q₃ = 165