Question

The city traffic police issued challans for not observing the traffic rules:

Day of the Week	Mon	Tue	Wed	Thus	Fri	Sat
No. of Challans	40	24	36	58	62	80

Find Q.D.

Answer 1

The given data can be arranged in ascending order as follows:
24, 36, 40, 58, 62, 80
Here, n = 6

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

= value of `((6 + 1)/4)^"th"` observation

= value of (1.75)^th observation
= value of 1^st observation + 0.75 (value of 2^nd observation – value of 1^st observation)
= 24 + 0.75(36 – 24)
= 24 + 0.75 (12)
= 24 + 9
∴ Q₁ = 33

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

= value of `3((6 + 1)/4)^"th"` observation

= value of (3 × 1.75)^th observation
= value of (5.25)^th observation
= value of 5^th observation + 0.25 (value of 6^th observation – value of 5^th observation)
= 62 + 0.25(80 –  62)
= 62 + 0.25(18)
= 62 + 4.5
= 66.5
∴ Q.D. = `("Q"_3 - "Q"_1)/2`

= `(66.5 - 33)/2`

= `(33.5)/2`

= 16.75