1

Problem

Identify any outlier(s) of the data set:
76, 72, 64, 93, 80, 78, 96, 75, 70, and 72.

2

Step

Order the data in ascending order

64, 70, 72, 72, 75, 76, 78, 80, 93, and 96.

3

Step

First, we have to find the first quartile and third quartile ranges Q1 and Q3:

→ Q1: The median of the lower half (64, 70, 72, 72, and 75)
Q1 = 72

→ Q3: The median of the upper half (76, 78, 80, 93, and 96)
Q3 = 80

4

Step

Calculate the Interquartile Range (IQR):

IQR = 80 - 72 = 8

5

Step

Identify potential outliers:

→ \$"Lower bound" = Q1 - 1.5 \times IQR = 72 - 1.5 \times 8\$ = 60

→ \$"Upper bound" = Q3 + 1.5 \times IQR = 80 + 1.5 \times 8\$ = 92

6

Step

Identify Outliers:

Any value below 60 or above 92 is an outlier
→ The dataset is: 76, 72, 64, 93, 80, 78, 96, 75, 70, and 72
→ The value 93 is above 92
→ The value 96 is above 92

7

Solution

Therefore, the outliers in this dataset are 93 and 96.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This option is incorrect because 96 is an outlier, but 94 is not an outlier it is within the upper bound

Wrong 94, 96

10

Choice-B

This option is incorrect because only 93 is questionable based on the IQR, and 92 is even lower than the data set

Wrong 93, 92

11

Choice-C

This option is incorrect because 95 is closer to the upper bound than 93, and 98 is a clear outlier beyond the IQR range

Wrong 95, 98

12

Choice-D

This option is correct because it is the most accurate answer. Both 93 and 96 fall outside the typical range of the data, based on IQR

Correct 93, 96

13

Answer

Option

D

14

Sumup

Please summarize choices