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# Outliers and their Effect on the Central Tendencies

Lesson 3 of 10

## Objective: SWBAT identify and verify outliers in a set of data and describe its effects on the Central Tendencies.

*50 minutes*

#### Partner Activity

*25 min*

To start this lesson, I hand each set of table partners a Football Activity to work together. It is an activity on identifying outliers by observation, and drawing conclusions about the effects on the Central Tendencies. I obtained this Activity at the following website:

https://www.google.com/search?q=classwork+1.9+examining+the+effect&oq=classwork+1.9+examining+the+effect&aqs=chrome..69i57.17958j0j7&sourceid=chrome&es_sm=91&ie=UTF-8 (last accessed 7-13-15)

Students have previously been introduced to outliers and their effects in the previous lesson. The purpose of this lesson is to provide students with more practice with outliers in a data set, and compare two methods when dealing with outliers. In the Football Activity, students are identifying the outliers by observation only.

I only assign students three pages of the Football Activity due to time constraints. I have students answer the questions to Data Set One (page one), Data Set Two (page three), and the Concluding Questions on the final page (page 7).

After reviewing the Partner Activity with the students, I provide students with notes on a second way to verify outliers using the 1.5 rule. The 1.5 rule is mostly used with a Box and Whisker Plot, but may be used with any set of data.

Below are two different student responses to question one in the Concluding Questions section of the assignment.

Student two is right about adding a large number will increase the mean, but not just by adding numbers. Student one also comments that the median will increase also, but not by how much. This student fails to recognize that the mean is affected much more than the median when a large number is added.

Student one talks about the mean sky rocketing, and does recognize that the effect on the mean is much more than just a change in the median.

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#### Guided Notes

*15 min*

After students complete the Football Activity with partners, I hand each student a copy of the Guided Notes. In the Guided Notes, I introduce the students to another way to identify an outlier by using the 1.5 rules. Students have previously identified the outlier by observation only based on their own intuition about a set of numbers.

When introducing students to the 1.5 rules, I emphasize that these rules are mostly used with Box and Whisker Plots. However, the 1.5 rules can be used with any set of data to verify outliers. In this lesson, we will not create Box and Whisker Plots. Instead we will use the set of data only to apply the 1.5 rules.

I demonstrate applying the 1.5 rules to a set of data in the video below.

#### Resources

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#### Exit Slip

*10 min*

After completing the Guided Notes with the students, I hand each student an Exit Slip. I use the Exit Slip as a quick formative assessment. I use it to check for student understanding of the two different methods to identify outliers in a set of data.

In Question One of the Exit Slip, students should recognize that by observation, the number 30 deviates from the numbers given. When looking at the data, it looks like that number 30 is an outlier.

So in Question Two, I have students verify that 30 is an outlier in the data set by using the 1.5 rules. Students do not have to create a Box and Whisker Plot. Students need to identify Quartile One and Quartile Three to apply the rules.

#### Resources

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Organizing and Calculating Data with Matrices
- LESSON 2: Introduction to Statistics
- LESSON 3: Outliers and their Effect on the Central Tendencies
- LESSON 4: Dot Plots, Box Plots, and Histograms! (Day 1 of 2)
- LESSON 5: Dot Plots, Box Plots, and Histograms! (Day 2 of 2)
- LESSON 6: Dispersion of Data (Day 1 of 2)
- LESSON 7: Dispersion of Data (Day 2 0f 2)
- LESSON 8: What is the Shape of the Data and What Can We Infer?
- LESSON 9: Analyzing Box and Whisker Plots in a Real World Context
- LESSON 10: Compare Two Data Sets Using Box and Whisker Plots