Pre-Algebra Unit 6: Measures of Central Tendencies

Unit Driving Question

How do data points affect mean and median in real-world situations? 

Essential Questions

1. What effects can changing data points have?

2. What influences the shape of the data?

Big Ideas

1. The mean and median of a data set is impacted by inserting or deleting data points.
2. Outliers can have an affect on measures of central tendency. 

Technology Resources

• Pre-Algebra Technology Resources

Launch Task

1 Lesson 

• Measures of Center(Geogebra): In this applet students will review data sets and the measures of central tendency. Students can move data points to discover the changes to mean, median, and mode.

Big Ideas for Development Lessons

2-3 Weeks (approximately 1 week per big idea)

Big Idea 1: The mean and median of a data set is impacted by inserting or deleting data points.

Key Resources 

1. Exploring Averages and Outliers(Geogebra): With this applet students will explore how changing data points impacts the measures of central tendency.

2. Exploring How Data Points Affect the Mean and Median : Students will explore patterns with adding a deleting data points on the mean and median.

3. Summarizing Center of Distributions(Khan Academy): A series of videos and practice questions that develop understanding for the insertion or deletion of a data point.

    

Big Idea Probe

• Unit 7: Big Idea 1 Probe

Evidence of Understanding 

Describe the impact that inserting or deleting a data point has on a data set

• The effects on the mean

• The effects on the median

Big Idea 2: Outliers can have an affect on measures of central tendency. 

Key Resources

1. Describing Data Sets with Outliers(Illustrative Mathematics): The goal of this task is to look at the impact of outliers on two important statistical measures of center: the mean and the median.

2. Exploring Averages, Box Plots, and Outliers(Geogebra): Using the same applet from lesson 1 in Big Idea 1, students will discover the effects of an outlier on a data set.

3. Effects of Outliers(CUSD80): This PDF document is a slide show with examples of the effects of outliers on measures of central tendency.

4. Guinness Outliers (Georgia Department of Education): Students will collect data and then use the world record to see how the outlier would affect the mean and median.

Big Idea Probe

• Unit 7: Big Idea 2 Probe 

Evidence of Understanding 

Explain how outliers affect the measures of central tendency

• The effects on the mean

• The effects on the median

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment) 

• Math Homework (OpenUp):  In this activity, students compare and contrast different measures of center and variability for data sets that have gaps and are not symmetrical.