Question

The daily wages (in Rs.) of 15 laboures are as follows:
230, 400, 350, 200, 250, 380, 210, 225, 375, 180, 375, 450, 300, 350, 250
Calculate D₈ and P₉₀.

Answer 1

The given data can be arranged in ascending order as follows:
180, 200, 210, 225, 230, 250, 250, 300, 350, 350, 375, 375, 380, 400, 450.
Here, n = 15

D₈ = value of `8(("n" + 1)/10)^"th"`observation

= value of `8((15 + 1)/10)^"th"`observation

= value of (8 × 1.6)^th observation
= value of (12.8)^th observation
=value of 12^th observation + 0.8 (value of 13^th observation – value of 12^th observation)
= 375 + 0.8 (380 – 375)
= 375 + 0.8 (5)
= 375 + 4
∴ D₈ = 379

P₉₀ = value of `90(("n" + 1)/100)^"th"`observation

= value of `90((15 + 1)/100)^"th"`observation
= value of (90 × 0.16)^th observation
= value of (14.4)^th observation
= value of 14^th observation + 0.4 (value of 15^th observation – value of 14^th observation)
= 400 + 0.4 (450 – 400)
= 400 + 0.4 (50)
= 400 + 20
∴ P₉₀ = 420