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# Practice with Measures of Central Tendency

Lesson 3 of 19

## Objective: SWBAT apply their understanding of the concepts from the first two lessons of the unit to questions dealing with measures of central tendency.

#### Opening

*15 min*

In this video I introduce my plan for today's work: Statistics_Day 3_Measures_of_Center

**Extensions/Scaffolds in this lesson: **In both the opening and closing activities, students can choose to discuss as many measures as they are able. In this case, students who have the ability to extend their thinking will be able to discuss all four measures of center while those that are still grappling with the concept may only discuss one or two. In either case, the tasks to open and close the lesson are accessible by all students in the class and give an entry point into the learning.

**Environment: **Students will be working in their partnerships once they do some initial thinking on their own. This collaboration will help them to further and deepen their understanding of the key concepts.

At the start of class we will be working from the Practice_Measures_of_Center presentation.

**Slide 2:** I like to bring in real world data whenever possible. This was a nice chart that shows the median household income in the United States. I put this slide up and ask students to write down as much information as then can by looking at this graph. Some students will make very surface level observations about the intervals and percentages. Other students will make more profound discoveries. I ask students to do a pair and share to get their ideas out and critique their partners thinking as well as their own. As they do this I walk around and listen for students who are talkig about the spread or distribution of the data (e.g. 50% of the data below the median, 50% above the median. The incomes above the median are much more "spread out" than those below, the data is "skewed" to the right, etc.). While this is not the topic of the day's lesson, it will help to plant the seed for box plots which will be the topic of the next lesson. Once students have an opportunity to share their thinking we move on to slide 3.

**Slide 3:** In this slide, I ask students to think about how adding a number to the data set can effect the measures of central tendency. This is somewhat backwards from what they are typically asked to do. Students have the analysis of the data, but no data. This forces them to abstractly think about what the data could look like in order to give them those measures. Students work on this by themselves first and then work with a partner to elaborate and further their original thinking. In actuality, an example can be given for any and all of the measures changing based on the new data point. I am looking for students to support their ideas with facts and explanations. This will help them to deepen their understanding of the four measures in general.

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#### Independent Practice

*25 min*

I will ask my students to work with a partner to complete the practice problems. Once students have had a sufficient time to work on the assignment, I will have students share out their answers and we will go over any questions that may have given students difficulty.

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#### Closure

*1 min*

To close today's lesson, we will go back to Slide 3 from the Practice_Measures_of_Center PowerPoint, we will discuss making a set of data that would have the four measures of central tendency given in this slide.

**What would adding a data point of 12 do to your four measures? **

This is a fairly challenging question that some students may struggle with. As a scaffold, allow students to make a data set that makes only 1 or 2 of the measures true. In doing this, I hope that my students will gain a greater understanding of the relationship between data and statistics. Extend their thinking to make a data set that makes all four measures true is a challenging task that often moves them forward in this regard.

#### Resources

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- LESSON 1: Asking a Statistical Question
- LESSON 2: Measures of Center
- LESSON 3: Practice with Measures of Central Tendency
- LESSON 4: Organizing Data with a Box Plot
- LESSON 5: Understanding Box Plots (with Assessment)
- LESSON 6: Analyzing a Box Plot
- LESSON 7: Constructing a Histogram
- LESSON 8: Modeling with Box Plots and Histograms
- LESSON 9: Connecting Box Plots and Histograms
- LESSON 10: What's this table saying?
- LESSON 11: Creating Two-Way Tables
- LESSON 12: More with Conditional, Joint, and Marginal Frequencies
- LESSON 13: Using a Scatterplot to Model Data
- LESSON 14: A Bivariate Relationship
- LESSON 15: Scatterplots and Non-Linear Data
- LESSON 16: Modeling with Non-Linear Data
- LESSON 17: Analyzing Residuals
- LESSON 18: Creating a Residual Plot
- LESSON 19: Got Ups? A Statistics Unit Task