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Question
Calculate D6 and P85 for the following data:
79, 82, 36, 38, 51, 72, 68, 70, 64, 63.
Solution
The given data can be arranged in ascending order as follows:
36, 38, 51, 63, 64, 68, 70, 72, 79, 82.
Here, n = 10
D6 = value of `6(("n" + 1)/10)^"th"`observation
= value of `6((10 + 1)/10)^"th"`observation
= value of (6 × 1.1 )th observation
= value of (6.6)th observation
= value of 6th observation + 0.6 (value of 7th observation – value of 6th observation)
= 68 + 0.6 (70 – 68)
= 68 + 0.6 (2)
= 68 + 1.2
∴ D6 = 69.2
P85 = value of `85(("n" + 1)/100)^"th"`observation
= value of `85((10 + 1)/100)^"th"`observation
= value of (85 × 0.11)th observation
= value of (9.35)th observation
= value of 9th observation + 0.35 (value of 10th observation – value of 9th observation)
= 79 + 0.35 (82 – 79)
= 79 + 0.35 (3)
= 79 + 1.05
∴ P85 = 80.05
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