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Question
The data gives number of accidents per day on a railway track. Compute Q2, P17, and D7.
4, 2, 3, 5, 6, 3, 4, 1, 2, 3, 2, 3, 4, 3, 2.
Solution
The given data can be arranged in ascending order as follows:
1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6
Here, n = 15
Q2 = value of `2(("n" + 1)/4)^"th"` observation
= value of `2((15 + 1)/4)^"th"` observation
= value of (2 x 4)th observation
= value of 8th observation
∴ Q2 = 3
P17 = value of `17(("n" + 1)/100)^"th"` observation
= value of `17((15 + 1)/100)^"th"` observation
= value of (17 x 0.16)th observation
= value of (2.72)th observation
= value of 2nd observation + 0.72 (value of 3rd observation – value of 2nd observation)
= 2 + 0.72 (2 – 2)
∴ P17 = 2
D7 = value of `7(("n" + 1)/10)^"th"` observation
= value of `7((15 + 1)/10)^"th"` observation
= value of (7 x 1.6)th observation
= value of (11.2)th observation
= value of 11th observation + 0.2 (value of 12th observation – value of 11th observation)
= 4 + 0. 2 (4 – 4)
∴ D7 = 4
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