1

Problem

Find any outliers in the test scores for a class:
55, 63, 70, 72, 61, 75, 80, 120, 60, 74, 68, 77, 65, and 76.

2

Step

Identifying Outliers in Test Scores:

→ This process helps us identify scores that are significantly different from the rest of the data set. These scores are called outliers 55, 63, 70, 72, 61, 75, 80, 120, 60, 74, 68, 77, 65, and 76.

3

Step

Order the data:

→ Arrange the test scores in ascending order
55, 60, 61, 63, 65, 68, 70, 72, 74, 75, 76, 77, 80, and 120.

4

Step

Find the quartiles:
For an odd number of data points (like this case with 14 scores)

→ The median of the lower half of the data set
→ Since we have 14 scores, the median is the 7th data point: Q1 = 63
→ The median of the upper half of the data set
Since we have 14 scores, the median is the 7th data point: Q3 = 76.

5

Step

Calculate the Interquartile Range (IQR):

IQR represents the spread of the middle 50% of the data
IQR = Q3 - Q1
Here, IQR = (76 - 63) = 13

6

Step

Determine the outlier thresholds:

→ Lower bound = \$Q1 - 1.5 \times IQR\$
→ Upper bound = \$Q3 + 1.5 \times IQR\$
In this case:
→ Lower bound = \$63 - 1.5 \times 13 = 63 - 19.5\$ = 43.5
→ Upper bound = \$76 + 1.5 \times 13 = 76 - 19.5\$ = 95.5

7

Step

Identify outliers:

Any test scores below 43.5 or above 95.5 are considered outliers. In this case:
→ Below 43.5: None

→ Above 95.5: 120

8

Solution

Therefore, the outlier in the test scores is 120.

9

Sumup

Please summarize steps

Choices

10

Choice-A

This option is incorrect because, 55 is potentially lower than the average, are not exceptionally distant from the rest of the data points compared to 120 based on the IQR method

Wrong Outlier: 55

11

Choice-B

This option is incorrect but, 80 is slightly close to the actual outlier but it is lower when compared to the actual outlier

Wrong Outlier: 80

12

Choice-C

This option is correct because, 120 is a clear outlier when using the IQR method

Correct Outlier: 120

13

Choice-D

This option is incorrect because 60 is potentially lower than the average, and not exceptionally accurate from the rest of the data points compared to 120 based on the IQR method

Wrong Outlier: 60

14

Answer

Option

C

15

Sumup

Please summarize choices