Compute Q3, D6, P70 for the following data: 28, 17, 12, 25, 26, 19, 13, 27, 21, 16

Posted: 18-07-2022

Answer:- Q3 = 26.25        D6 = 23.4         P70 = 25.7

Step-by-step explanation:

Firstly, arranging the data in ascending order, we get,

12, 13, 16, 17, 19, 21, 25, 26, 27, 28

Q3 characterize third quartile in the data.

The formula for calculating Q3 = observation where n is number of observations in the data.

Q3 = obs. = 8.25th obs.

8.25th obs = 8th obs + 0.25*(9th obs – 8th obs)

= 26 + 0.25*(27 – 26) = 26.25

Consequently, third quartile, Q3 = 26.25.

D6 characterize sixth decile in the data.

The formula for calculating D6 = obs.

= obs. = 6.6th obs.

6.6th obs = 6th obs + 0.6*(7th obs – 6th obs)

= 21 + 0.6*(25 – 21) = 23.4

Therefore sixth decile, D6 = 23.4 .

P70 represent 70th percentile in the data.

 The formula for calculating P70 = obs.

P70 = obs = 7.7th obs.

7.7th obs = 7th obs + 0.7*(8th obs – 7th obs)

= 25 + 0.7*(26 – 25) = 25.7

Therefore 70th percentile,P70 = 25.7 .