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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.
Solution
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 1st observation + 0.75 (value of 2nd observation – value of 1st 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 5th observation + 0.25 (value of 6th observation – value of 5th 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
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