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# 12.3: Box Plots & Histograms

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Algebra I, Chapter 11, Lesson 8.

ID: 8200

Time required: 30 minutes

## Activity Overview

Students create and explore a box plot and histogram for a data set. They then compare the two data displays by viewing them together and use the comparison to draw conclusions about the data.

Topic: Data Analysis and Probability

• Represent and interpret data displayed in data graphs including bar graphs, circle graphs, histograms, stem-and-leaf plots and box-and-whisker plots.
• Display univariate data in a spreadsheet or table and determine the mean, mode, standard deviation, extrema and quartiles.

Teacher Preparation and Notes

• This activity is appropriate for students in Algebra 1. It assumes that students are familiar with mean, median, minimum, interquatile, etc.
• This activity is intended to be teacher-led with students in small groups. You should seat your students in pairs so they can work cooperatively on their calculators. You may use the following pages to present the material to the class and encourage discussion. Students will follow along using their calculators.
• The student worksheet is intended to guide students through the main ideas of the activity. It also serves as a place for students to record their answers. Alternatively, you may wish to have the class record their answers on separate sheets of paper, or just use the questions posed to engage a class discussion.

Associated Materials

Before beginning the activity, the list WKND needs to be transferred to the students’ calculators or students need to store the numbers given on the worksheet to a list titled WKND.

If you choose to have students store the numbers manually, they need to press STAT ENTER to access the List Editor. Then arrow to the top of L1\begin{align*}L1\end{align*} and arrow over to the top of the 7th list which has no heading. The calculator will be in Alpha Mode, so students are to type the heading WKND. Then enter the numbers as usual.

## Part 1 – Create a box plot

First students will set up and investigate a box plot of the distances in the WKND list using Plot1. They should make sure that all other plots and equations have been turned off.

The window settings that are given on the worksheet will enable students to view the box plot and the histogram later in the activity without having to change the settings.

After answering the questions on the worksheet students will draw a vertical line on the graph to show where the mean is located in the box plot compared to the median.

## Part 2 – Create a histogram

Now students will set up and investigate a histogram of the distances in the WKND list using Plot2. They need to turn off Plot1 (the box plot) before viewing the graph.

The Xscl of the graph is 20\begin{align*}20\end{align*}. Explain to students that this means each bar is an interval of 20\begin{align*}20\end{align*} (i.e., to 19\begin{align*}19\end{align*}, 20\begin{align*}20\end{align*} to 39\begin{align*}39\end{align*}).

After answering the questions on the worksheet, students will draw two vertical lines, one for the mean and one for the median of the distances.

Using the commands mean(LWKND) and median(LWKND) on the Home screen will allow students to see the exact values of the mean and median (67.83\begin{align*}67.83\end{align*} and 51\begin{align*}51\end{align*}, respectively).

## Part 3 – Compare a box plot and a histogram

Students are directed to turn Plot1 (box plot) back on so that they can view the box plot and histogram on the same screen.

Use this view to guide a discussion about the relationship between the box plot and the histogram. Begin with more obvious connections—a taller bar in the histogram corresponds with more points on the box plot than a shorter bar, for example. Then lead students to make deeper conclusions about the shape of the data. (For example, it is grouped mostly in the lower values; the data contains many distances close together on the low end of the scale and relatively few larger distances; the larger distances are more spread out.)

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