# Box Plots and Distributions

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## Objective

SWBAT compare the distributions of two data sets by creating box plots.

#### Big Idea

A graph is a visual representation that can be used to analyze and interpret data based on the center, spread and overall shape of the data.

7 minutes

As this class begins students complete the Think About It problem independently.  The idea of this problem is to get kids thinking about Box Plots, which they learned in the previous unit.  Students shouldn't struggle with these questions.

After 3 minutes of work time, I have students compare their responses with their partners (see the student sample).  I then display the correct answers on the document camera and allow students to ask any clarifying questions they may have.  At this point in the year, if there are any clarifying questions, I expect the class to answer them (rather than have me respond).

Before moving on I frame the lesson by letting students know that they will be learning how to analyze and interpret two sets of data using a two box plots that are drawn on the same number line in this lesson.  This is an important skill because it will allow you to make decisions between two choices based on facts and data.

## Intro to New Material

15 minutes

(Students learned how to create box plots in an earlier lesson.  You may wish to provide students with copies of the Key Vocabulary, which students learned in the previous unit.)

To start today's Intro to New Material section, I have students complete the five number summaries for both homerooms in Example 1.

Homeroom 1 has a greater range. I'll ask the class what that means in the context of this problem?

A possible response:  homeroom 1 is less reliable, there is huge variability.

At this point I expect some kids to really get it, but some kids will not.  I'll cold call on a student to share the IQR for each homeroom, and then ask a student to explain what those numbers mean, given the context of the problem.

A possible response:  Homeroom 1 had a greater spread for the middle 50%. Where as in homeroom 2 the middle 50% scored around the same score.

I'll also ask everyone to write a response to Question B, which asks, "Which homeroom performed better on this exam?"  I'm looking for students to respond that Homeroom 1 performed better, overall.  Evidence that students can use should include the mean, and the position of the quartiles (75% of the kids in Homeroom 1 performed as good or better than the mean of Homeroom 2).  Students might also write about the upper extreme, although this is not a strong piece of evidence on its own.

After this discussion students will move on to Example 2, again completing the 5 number summaries for each data set.  I'll then have students construct a double box plot on the provided number line.  While creating the double box plot, students follow a similar process to what they have used before:

1. Arrange the data in order from least to greatest (if not already in order).
2. Find the maximum, minimum, median, 1st quartile, and 3rd quartile for each data set.
3. Label the number line if necessary using an appropriate scale for both sets of data.
4. Draw the ends of the two whiskers at the maximum and minimum for each data set.
5. Mark the 1st and 3rd quartile and use those markings to draw the box for each data set.
6. Draw the median line for each data set.

My students will struggle the most with Step 3. To tackle this, I allow for students to try to use different intervals to see what will make the most sense for both sets of data and push students to justify the scale that they chose.

## Partner Practice

15 minutes

As usual , students work with their partners on the Partner Practice problem.  Students have access to calculators as they work.  As they work, I circulate around the classroom and check in with each group.  I am looking for:

• Have students correctly identified the five number summary for both sets of data?
• Have they created a number line with reasonable intervals?
• Have students correctly created and labeled two box plots to represent the data sets?
• Have students drawn the correct conclusions about the relationship of the two box plots?
• Are students correctly interpreting and analyzing the data?

• How did you determine the five number summary?
• How did you determine which scale to use?
• How did you create the two box plots?
• How did you know what percent represents <insert the desired information>?

Students have 10 minutes to work on the Partner Practice problem.  They then complete the Check for Understanding problem independently.  This CFU sample shows what student work could look like. I have the class share out responses for the CFU.  For each problem, students vote for either TastiSnak or Harvest Time.  I then cold call a student to share his/her explanation.

## Independent Practice

15 minutes

As students work on the Independent Practice problem set, I am looking to see how they perform on the new skill in this lesson: writing a conclusion based on a statistical comparison.  As I circulate, I will read over student responses and provide feedback.  This work sample provides an example of a strong student response.

## Closing and Exit Ticket

8 minutes

After independent work time, I have students talk to their partners in response to this question:

Why might someone decide to use two box plots?

Students might say -  Box plots are useful because they give us a 5 number summary for which we can compare two data sets. Students then complete the Exit Ticket independently to close the lesson.

A top quality student response for Question 1 might resemble:  Super Fit had an attendance between 48 and 82. The Athletic Club had an attendance between 57 and 110. The attendance at the Athletic club varies more than the attendance at Super Fit.