Question

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

Answer 1

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

Solution :-

Total terms are :- 15.

Now, arranging given data in ascending order :- 180, 200, 210, 225, 230, 250, 250, 300, 350, 350, 375, 375, 380, 400, 450.

Now we know that,

• D(k) = value of k(n+1/10)th observation where k = 1,2,3____9.
• P(k) = value of k(n+1/100)th observation where k = 1,2,3____99.

So,

→ D(8) = value of 8(n + 1/10)th observation .

→ D(8) = 8 * {(15 + 1)/10}th observation.

→ D(8) = (8 * 1.6)th observation.

→ D(8) = (12.8)th observation.

→ D(8) = 12th observation + 0.8(13th observation - 12th observation)

→ D(8) = 375 + 0.8(380 - 375)

→ D(8) = 375 + 0.8 * 5

→ D(8) = 375 + 4

→ D(8) = 379 (Ans.)

Similarly,

→ P(90) = value of k(n+1/100)th observation.

→ P(90) = value of 90(15+1/100)th observation.

→ P(90) = (90 * 0.16)th observation.

→ P(90) = (14.4)th observation

→ P(90) = 14th observation + 0.4(15th observation - 14th observation)

→ P(90) = 400 + 0.4(450 - 400)

→ P(90) = 400 + 0.4 * 50

→ P(90) = 400 + 20

→ P(90) = 420 (Ans.)

Hence, D(8) is 379 and P(90) is 420.

Answer 2

Answer:

assessing order

180,200,210,225,230,250,,300,350,350,375,375,380,400,450

n=15

D8=8 x15+1 divide by 10

8 x 16 divideby 10

128 divide by 10

12.8th term

12th term +0.8 x13th term _12th term

375 +0.8 x ( 380 - 3 75)

375 + 0.8 x 5

375+40

D 8 = 379

P90=90 x n + 1 divide by 100

90 x 16 divide by 100

1440 divide by 100

14. 40 th term

400+0.40 x 450 - 400

400 + 0.40 X50

400 + 20.00

P90=420