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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Box and Whisker Plots, Identifying Outliers

Grade: 1300-a Lesson: S4-L6

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
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 = 65. → The median of the upper half of the data set. Since we have 14 scores, Q3 is the average of the 8th and 9th data points: Q3 = \$(74 + 75) / 2\$ = 74.5.
5	Step	Calculate the Interquartile Range (IQR) IQR represents the spread of the middle 50% of the data. IQR = Q3 - Q1. Here, IQR = (74.5 - 65) = 9.5.
6	Step	Identify potential outliers → \$"Lower bound": "Q"1 - 1.5 \times "IQR"\$ → \$"Upper bound": "Q"3 + 1.5 \times "IQR"\$ In this case: → \$"Lower bound" = 65 - 1.5 \times 9.5 = 48.25\$ → \$"Upper bound" = 74.5 + 1.5 \times 9.5 = 91.75\$
7	Step	Analyze the outliers The test score of 120 is significantly higher than the upper bound (91.75).
8	Step	Therefore, the test score of 120 is considered an outlier in this data set.
9	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	outlier: 55
10	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	outlier: 80
11	Choice.C	This option is correct because,120 is a clear outlier when using the IQR method	outlier: 120
12	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	outlier: 60
13	Answer	Option	C
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

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.

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.

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.

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 = 65.
→ The median of the upper half of the data set.
Since we have 14 scores, Q3 is the average of the 8th and 9th data points:
Q3 = \$(74 + 75) / 2\$ = 74.5.

Step

Calculate the Interquartile Range (IQR)
IQR represents the spread of the middle 50% of the data.
IQR = Q3 - Q1.
Here, IQR = (74.5 - 65) = 9.5.

Step

Identify potential outliers
→ \$"Lower bound": "Q"1 - 1.5 \times "IQR"\$
→ \$"Upper bound": "Q"3 + 1.5 \times "IQR"\$

In this case:
→ \$"Lower bound" = 65 - 1.5 \times 9.5 = 48.25\$
→ \$"Upper bound" = 74.5 + 1.5 \times 9.5 = 91.75\$

Step

Analyze the outliers
The test score of 120 is significantly higher than the upper bound (91.75).

Step

Therefore, the test score of 120 is considered an outlier in this data set.

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

outlier: 55

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

outlier: 80

Choice.C

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

outlier: 120

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

outlier: 60

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?