Maharashtra State BoardHSC Commerce 11th
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The daily wages (in Rs.) of 15 laboures are as follows:230, 400, 350, 200, 250, 380, 210, 225, 375, 180, 375, 450, 300, 350, 250Calculate D8 and P90. - Mathematics and Statistics

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Sum

The daily wages (in Rs.) of 15 laboures are as follows:
230, 400, 350, 200, 250, 380, 210, 225, 375, 180, 375, 450, 300, 350, 250
Calculate D8 and P90.

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Solution

The given data can be arranged in ascending order as follows:
180, 200, 210, 225, 230, 250, 250, 300, 350, 350, 375, 375, 380, 400, 450.
Here, n = 15

D8 = value of `8(("n" + 1)/10)^"th"`observation

= value of `8((15 + 1)/10)^"th"`observation

= value of (8 × 1.6)th observation
= value of (12.8)th observation
=value of 12th observation + 0.8 (value of 13th observation – value of 12th observation)
= 375 + 0.8 (380 – 375)
= 375 + 0.8 (5)
= 375 + 4
∴ D8 = 379

P90 = value of `90(("n" + 1)/100)^"th"`observation

= value of `90((15 + 1)/100)^"th"`observation
= value of (90 × 0.16)th observation
= value of (14.4)th observation
= value of 14th observation + 0.4 (value of 15th observation – value of 14th observation)
= 400 + 0.4 (450 – 400)
= 400 + 0.4 (50)
= 400 + 20
∴ P90 = 420

Concept: Relations Among Quartiles, Deciles and Percentiles
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