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# Connecting Box Plots and Histograms

Lesson 9 of 19

## Objective: SWBAT determine the approximate locations of the quartiles in a data set using both a histogram and a box plot.

## Big Idea: This lesson allows students to build meaning about the connection between how distributions are displayed in box plots and histograms.

*50 minutes*

#### Investigation

*30 min*

**Extention/scaffolds: **Students are asked to explain their ideas and thoughts during the investigation portion of this lesson. Due to the constructivist nature of the activity, no scaffolds are in place up front. Some students may need addtional support during the lesson. Also, the extention is built into the activity due to the fact that students will make more sophisticated observations.

*Phase 1*: Students will work with their partner to pair the histogram, box plot and verbal description. I do not give students any other information other than the task at hand, I want them to construct the meaning of why the different cards go together. (Note, each card has a number, letter, or symbol to make checking the matches quick for the teacher.)

*Phase 2:* Students work in pairs to write a complete description of why they made the matches that they did. In their description they should make specific references to the distribution of the data including the quartiles and median and how they are graphically displayed in the histogram.

**Teaching point:** It is important that students reference the specific number of students in each interval as well as noting the percentages of the class 25%, 50%, 75%, etc. This will help to deepen the connection that box plots represent the data being broken into 4 sections with an equal amount of data in each. When the intervals on the box plot are small it means that there are many data points in a smaller interval (spread of data). This lesson is also a good time to discuss the idea of "skew" of data due to the fact that it can be easily seen in the histograms and box plots when they are put side by side.

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#### Closure

*10 min*

*slide 3: *Students will analyze this box plot and write a verbal description about the monthly spending of the students. Students should apply what they have just learned from the investigation regarding the distribution of the data.

#### 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