Question

Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 64 64 61 57 58 60 62 54 56 58 56 58 65 65 80

Answer 1

a) First we have to write the data in ascending order

54,56,56,57,58,58,58,60,61,62,64,64,65,65,80

The first quartile is Q1 = (N+1)/4 th observation

Q1 = (15+1)/4th observation = 4 th observation

Q1 = 57

The second quartile Q2 = (N+1)/2 th observation

Q2 = 8th observation

Q2 = 60

The third quartile Q3 = 3(N+1)/4 th observation

Q3 = 3(15+1)/4 th observation = 12 th observation

Q3 = 64

b) The interquartile range is IQR = Q3 - Q1 = 64 - 57

IQR = 7

c) The outlier is indentify using the range

Outlier < Q1 - 1.5*IQR and Q3 + 1.5*IQR < Outlier

Q1-1.5*IQR = 57- 1.5*7 = 46.5

Q3+1.5*IQR = 64 + 1.5*7 = 74.5

So only 80 is the observation > Q3 + 1.5*IQR

80 is outlier