Question

122. Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the Table 2.83.

# of books Freq. Relative Freq.

0 18   

1 24

2 24

3 22

4 15

5 10

7 5

9 1

a. Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.

Answer 1

Answer:

Given that,

Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the table.

# of books	Frequency	Cumulative frequency
0	18	18
1	24	42
2	24	66
3	22	88
4	15	103
5	10	113
7	5	118
9	1	119
Total	119

From the cumulative frequency column, get the three quartiles

Q1 is the data value below which 25% of the data lies.

Position of Q1 is 119/4= 29.75th value

Position of Q2 is 2(119/4)=59.50th value

Position of Q3 is 3(119/4)=89.25th value

Thus,

29.75th value in cumulative frequency is between 0 and 1. Hence Q1=0.5

59.50th value in cumulative frequency is between 1 and 2. Hence Q2=1.5

89.25th value in cumulative frequency is between 3 and 4. Hence Q3=3.5

Interquartile range (IQR) is given by,

IQR=Q3-Q1

IQR=3.5-0.5=3

Interquartile range (IQR)=3

1.5 IQR=1.5 3 =4.5

Q1-1.5 IQR=0.5-45=-4

Q3+1.5 IQR=3.5+4.5=8

No value for number of books is less than -4.

However, there is one value which is 9, that is greater than 8.

Therefore, 9 books are an outlier value.