Question

5. Students from an English class were asked to record their heights in inches. Their heights were:

65, 72, 69, 64, 60, 55, 72, 71, 52, 63, 60, 74, 69, 67, 74, 50, 44, 75, 67, 62, 66, 81, 64, 65

a. Find the mean.

b. Identify the five number summary

c. Determine if there are any outliers.

Answer 1

Write data in ascending order,

44, 50, 52, 55, 60, 60, 62, 63, 64, 64, 65, 65, 66, 67, 67, 69, 69, 71, 72, 72, 74, 74, 75, 81

a)

Mean = X / n

= 1561 / 24

= 65.0417

b)

Minimum = 44

Q1 = ( n + 1) / 4 th observation

= ( 24+1) / 4

= 6.25 th observation

= 60.50

Q2 = (n + 1) / 2 th observation

= ( 24 + 1) / 2

= 12.5 th observation

= 65.5

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

= 3 ( 24 + 1) / 4

= 18.75 th observation

= 71.75

Maximum = 81

Five number summery = Min , q1 , Q , Q3 , Max = 44 , 60.5 , 65.5 , 71.75 , 81

c)

IQR = Q3 - Q1 = 71.75 - 60.5 = 11.25

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

Q1 - 1.5 IQR = 60.5 - 1.5 * 11.25 = 43.625

Q3 + 1.5 IQR = 71.75 + 1.5 * 11.25 = 88.625

Outliers = No outliers