Question

Question 1: There's a sample of10 people with ages

5

39

75

79

85

90

91

93

93

98

a. Draw a box plot (Find lower and upper – inner and outer fences).

b. Determine mild outliers.

c. Determine extreme outliers.

Answer 1

Ans:
a)
5,39,75,79,85,90,91,93,93,98
Median: 87.5
Minimum: 5
Maximum: 98
First quartile: 66
Third quartile: 93
Interquartile Range: 27



b)inner fences are 66-1.5*27=25.5 and 93+1.5*27=133.5
There is one mild outlier i.e. 5,as 5 is below 25.5
c)lower and upper fence are 66-3*27=-15 and 93+3*27=174
No extreme outlier,as all data values are within fences

Note:
For  Mild outlier:
 Q1 - 3 * IQR <= x < Q1 - 1.5 * IQR

or

   Q1 + 1.5 * IQR < x <= Q3 + 3 * IQR

For extreme outlier:

   x < Q1 - 3 * IQR   
or

   x > Q3 + 3 * IQR