Question

3] Find Quartiles D7, P47 for the following data: 79,82,36,38,51,72,68,70,64,63​

Answer 1

Answer:

Step-by-step explanation:Question :- find D8 and P85 for the following data 79,82,36,38,51,72,68,70,64,63 ?

Solution :- Total terms are 10.

Arranging them in ascending order = 36, 38, 51, 63, 64, 68, 70, 72, 79 and 82.

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 * {(10 +1)/10]th observation.

→ D(8) = (8 * 1.1)th observation.

→ D(8) = (8.8)th observation.

→ D(8) = 8th observation + 0.8(9th observation - 8th observation)

→ D(8) = 72 + 0.8(79 - 72)

→ D(8) = 72 + 0.8 * 7

→ D(8) = 72 + 5.6

→ D(8) = 77.6 (Ans.)

Similarly,

→ P(85) = value of k(n+1/100)th observation.

→ P(85) = value of 85(10+1/100)th observation.

→ P(85) = (85 * 0.11)th observation.

→ P(85) = (9.35)th observation

→ P(85) = 9th observation + 0.35(10th observation - 9th observation)

→ P(85) = 79 + 0.35(82 - 79)

→ P(85) = 79 + 0.35 * 3

→ P(85) = 79 + 1.05

→ P(85) = 80.05 (Ans.)

Hence, D(8) and P(85) of the given data is 77.6 and 80.05.

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