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# Understanding Box Plots (with Assessment)

Lesson 5 of 19

## Objective: SWBAT analyze a box plot in order to determine the five number summary as well as the distribution of the data.

#### Opening

*10 min*

During the first ten minutes of class, I will pose a few review problems for students using box_plot_day2*.*

As we view Slide 2, students will work with their partners to review the vocabulary from the previous lesson. They will also find the 5 number summary (min, 1st quartile, median, 3rd quartile, max) necessary for constructing a box plot. Once students find the five number summary they will verify with their partner that they have divided the data set into four equally-sized portions.

Slide 3 requires students to problem solve within their partnerships. The students are going to find the interquartile range, but from a more abstract perspective. This is because none of the actual data points are given to the students. The only information I have given the students is the frequency table.

**Teaching Point: **Some students will be able to visualize how the 19 scores are distributed, however, some will not. For students who struggle it I guide them to make 19 tally marks to represent the data points written in order. This way they can find the median and two quartiles in a more concrete way seeing that the median will be the 10th data point, the 1st and 3rd quartiles will be the 5th and 15th data points respectively. Students can then go back to the frequency table to determine in which intervals these values lie.

The box plot on Slide 4 represents the weights of our 2013 high school football team. I ask students to work on their own to analyze this box plot and write down any inferences that they are able to make from the plot. Then, I will ask them to share their results with their partner. Before we move on to the assessment, we will share out a few of the ideas with the class.

Finally, I pose the following question to the class:

**True or False**: Most of the team weighs between 205 and 320. Explain why this is true or false.

Students discuss this with their partners. Through a group share out we want to dispell the misconception that if a section of a box plot is larger than another that it contains more data points.

#### 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