Question

Shown below are the total number of medals won by the top 13 countries ordered based on the number of gold medals won in the 2000 Olympic games as of September 25, 2000.
58, 48, 47, 43, 31, 28, 19, 15, 19, 29, 13, 18, 9

According to the 1.5xIQR rule which one(s) of these observations are suspected outliers??

58, 48

None

58

58, 9

58, 48, 47

9

Answer 1

Sort the sample by ascendin order.

9, 13 , 15 , 18, 19 , 19 , 28 , 29 , 31 , 43 , 47 , 48 , 58

First quartile Q1 = (n+1) / 4 th obswervation.

= (13 + 1) /4

= 3.5th observation

= 16.5

Q1 = 16.5

Third quartile Q3 = 3(n+1) / 4 th observation

= 3(13+1) / 4

= 10.5 th observation

= 45

Q3 = 45

Interquartile range IQR = Q3 - Q1

= 45 - 16.5

IQR = 28.5

Outliers are the observations less than Q1 - 1.5 IQR or more than Q3 + 1.5 IQR

Q1 - 1.5 IQR = 16.5 - 1.5 * 28.5 = -26.25

Q3 + 1.5 IQR = 45 + 1.5 * 28.5 = 87.75

Outliers are observatios less than -26.25 or more than 87.75

There are no such outlier in given sample.

According to 1.5*IQR rule, number of outliers = None