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Question
Solve the following:
Calculate Q1, D4, and P26 for the following data.
| 18, 24, 45, 29, 4, 7, 28, 49, 16, 26, 25, 12, 10, 9, 8 |
Solution
Q1 = size of 1`((n+1)/4)^"th observation"`
Q1 = size of 1`((15+1)/4)^"th observation"`
Q1 = Size of 1 `(16/4)^"th observation"`
Q1 = Size of 1(4)th observation
Size of the 4th observation = 9
Q1 = 9
D4 = Size of 4 `((n+1)/10)^"th observation"`
D4 = Size of 4`((15+1)/10)^"th observation"`
D4 = Size of 4`(16/10)^"th observation"`
D4 = Size of 4(1.6)th observation
= Size of 6.4th observation
= Size of 6th observation + 0.4 (7th observation – 6th observation)
= 12 + 0.4 (16 - 12)
= 12 + 0.4 (4)
= 12 + 1.6
= 13.6
D4 = 13.6
P26 = Size of 26`((n+1)/100)^"th observation"`
P26 = Size of 26`((15+1)/100)^"th observation"`
P26 = Size of 26`(16/100)^"th observation"`
= size of 26 (0.16)th observation
= Size of 4.16th observation
= size of 4th observation + 0.16(5th observation - 4th observation)
= 9 + 0.16 (10 - 9)
= 9 + 0.16(1)
= 9 + 0.16
= 9.16
P26 = 9.16
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