Problem 4

4. Determine the median and values corresponding to the first and third quartiles in the following data.
5.24
6.02
6.67
7.3
7.59
7.99
8.03
8.35
8.81
9.45
9.61
10.37
10.39
11.86
12.22
12.71
13.07
13.59
13.89
15.42 Median = 9.45 +9.91 / 20 = 9.53
Lp=(n+1)(P/100)
L25=(20+1)(25/100)
L25=5.25
L75=(20+1)(75/100)
L75=15.75
The 1st quartile is located between the 5th and the 6th value. The distance between 1st and 6th value is 0.40. Then we multiply 0.40(0.25) = 0.10. Finally we add 0.10 to the Q1 = 7.69
The 3rd quartile is located between the 15th and the 16th value. The distance between 15th and 16th is 0.49. The we multiply 0.49(0.75)=0.367. Finally we add 0.367 to the Q3 = 12.59