# Constructing a Histogram

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## Objective

SWBAT use a frequency histogram to organize and interpret data.

#### Big Idea

Students get to experience the collection and organization of data.

## Opening

15 minutes

Today, I will have students work in heterogeneous groups.  However, students who are going to work with the scaffolded data collection worksheet should be paired. It is important for them to work with the same frequency table when constructing a histogram.

To begin the lesson, I will select the first student enters the room as the recorder.  As the recorder, their responsibility is to write down each following student's height in inches in the order that they enter the classroom. (This simulates a random process.) I will have Slide 2 (height conversions -- feet to inches) posted to assist the recorder in collecting quick, accurate data on student heights in inches.

Once the data is collected, I will call the class to attention and ask students what they remember about histograms.  Usually someone will offer, "A histogram is like a bar graph." From this point, I like to ask the class if anyone knows the difference. If not, I explain that this is a good comparison, but bar graphs typically present with discrete, categorical data while histograms usually represent the distribution of a numerical data set.

As an example of a Histogram, I present a graphic showing the daily high temperatures for April 2014 in Buffalo. I present the data set, then the histogram.  I ask students to take a moment to observe the graphic and write down in their notebooks how the histogram was constructed from the data set (MP3).  After giving the students time to work on their own, I ask them to share their answers with a partner (Think-Pair-Share).  To end this reflection activity, I will select one partnership to share out and then ask for others to add to the original ideas.

During the whole class conversation, I am hoping to hear students share the data is broken up into intervals, and, the number of data points in each interval is tallied.  Before moving on with the lesson, I may ask students to take two minutes to write down everything they feel is important about making a histogram. The big four for me are:

1. Bars are touching (continuous data)
2. Show space (or break the graph) before the first interval if the data does not start at zero
3. Include Labels on both axes  as well as a title
4. Make sure to use an appropriate scale (interval width and y-axis spacing as needed) (MP6).

## Investigation Part 1

10 minutes

To begin today's investigation (see stats_histogram_day1)students create a frequency table to summarize the height data that we collected at the beginning of class. Choosing the width of the intervals is an important skill,  so I ask students to choose the intervals themselves. I encourage them to think carefully so that they don't end up with too many or too few. In my mind, selecting these intervals is important because it helps students to visualize how the data will ultimately be organized.  After they complete the frequency table, each student proceeds to create a histogram representing the data. Once students construct their histograms, I plan to show some examples representing different interval choices on the document camera. Students typically have a lot to say about how the choice of intervals affects the shape of the graph. So, we will discuss and share ideas as histograms are presented.

Scaffolds: For students who struggle with number sense, I will fill in the frequency tables and cumulative frequency tables with the intervals ahead of time.  I know that most students in ninth grade are between 58 inches and 76 inches tall, so it is relatively easy to prepare a frequency table in advance. I scaffold the activity in this way so that my students can concentrate on how the data will be organized into each interval and the shape of the data set, since this is an important part of the story.

## Direct instruction & Investigation Part 2

15 minutes

To follow the first investigation, I like to teach students how to create a Cumulative Frequency Table. Slide 4 in the Stats_Histogram_Day 1 presentation is a placeholder, that I can use if necessary. I plan to display a student's frequency table using the document camera and talked through the process of creating a cumulative frequency from an existing students work.

After I demonstrate the process, I will ask my students design and graph a cumulative frequency histogram and box plot (see Histogram Worksheet). When making the box plot, it is important that students choose an appropriate scale for the x-axis so that the box plot itself is drawn to scale.

The check for understanding at the end of the Worksheet will assess whether or not students understand the structure and use of a cumulative frequency table.

5 minutes