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 .