Question

check each data set for outliers a. 46, 28, 32, 21, 25, 29, 34, 19 b. 82, 100, 97, 93, 89, 90, 65, 94, 101 c. 527, 1007, 489, 371, 175

Answer 1

a) Arrange the given data in ascending order

1	19
2	21
3	25
4	28
5	29
6	32
7	34
8	46

Q1 = (21 + 25)/2 = 23

Q3 = (32 + 34)/2 = 33

IQR = 33 - 23 = 10

Lower fence = Q1 - 1.5*IQR = 23 - 1.5*10 = 8

Lower fence = Q1 + 1.5*IQR = 23 + 1.5*10 = 38

For this data set 46 is an outlier

b)

1	65
2	82
3	89
4	90
5	93
6	94
7	97
8	100
9	101

Q1 = (82 + 89)/2 = 85.5

Q3 = (97 + 100)/2 = 98.5

IQR = 98.5 - 85.5 = 13

Lower fence = Q1 - 1.5*IQR = 85.5 - 1.5*13 = 66

Lower fence = Q1 + 1.5*IQR = 98.5 + 1.5*13 = 118

For this data set 65 is an outlier

c)

1	175
2	371
3	489
4	527
5	1007

Q1 = (175 + 371)/2 = 273

Q3 = (527 + 1007)/2 = 767

IQR = 767 - 273 = 494

Lower fence = Q1 - 1.5*IQR = 273 - 1.5*494 = -468

Lower fence = Q1 + 1.5*IQR = 767 + 1.5*494 = 1508

For this data set there is no outlier