Histograms As A Tool To Describe Data

Histograms As A Tool To Describe Data

Sixth Graders Swimming Under Water

Opening

Sixth Graders Swimming Under Water

Look at the line plot. It shows data collected in a sixth grade class about how long students can swim underwater.

Discuss the following questions with your partner:

  • Can you easily see the shape of the data?
  • What might you do in order to see the shape of the data better?

Make a Histogram

Opening

Make a Histogram

A histogram is a graph that shows data in intervals of equal size.

As a class, make a histogram for the data in the “How Long Can Sixth Grade Students Swim Under Water?” line plot. Use these steps:

  • Decide on a range for each bin. This range is called the bin width, and it should be the same for each bin.
  • Determine the number of data points in each bin.
  • Draw a horizontal and vertical axis.
  • Look at the highest number of data points in your bins, and use that number to determine your scale for the vertical axis.
  • Divide the horizontal line into intervals based on your data and bin width.
  • Label the vertical and horizontal lines and create a title for your histogram.

Math Mission

Opening

Make a histogram to show the distribution of your data for sixth grade students.

Represent Data in a Histogram

Work Time

Represent Data in a Histogram

  • Make a histogram using the data you collected on your typical six grade student question.
    • Decide what the range of each bin should be.
    • Determine the number of data points in each bin.
    • Create a frequency scale on the vertical line.
    • Divide the horizontal line into intervals based on your bin width.
    • Label the vertical and horizontal lines and create a title for your histogram.
  • Write a summary of what your histogram shows about your data.
  • How do you think your histogram would look if you used different intervals?

Hint:

  • Each group of data in a histogram is called a bin . Each bin “fills up” with the data that belong in that bin. For example, in a histogram that represents height, each bin represents a range of heights.
  • To make a histogram, you need to first decide the bin width. Each bin should be the same width.
  • Remember that the bars in a histogram should touch each other.

Prepare a Presentation

Work Time

Prepare a Presentation

Discuss how you decided what bin width to use for your histogram and how you divided the horizontal line into intervals. Explain what your histogram tells you about a typical sixth grade student.

Challenge Problem

  • What would a histogram with a bin width of 1 look like?
  • What would a histogram with a bin width that is equal to the range look like?

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes as your classmates present their histograms.

Hint:

As your classmates present, ask questions such as:

  • How did you decide what bin width to use for your histogram?
  • What problems did you have in creating the histogram for your data about a sixth grade student? How did you deal with those problems?
  • Can you explain what your histogram tells us about your data for a sixth grade student?

All About Histograms

Formative Assessment

Summary of the Math: All About Histograms

Read and Discuss

  • Unlike with line plots, measures of center and spread cannot be found by looking at a histogram, because individual data values are not shown. The number of data points in a histogram can be found by adding the frequencies of the bins.
  • To make a histogram, you have to choose a bin width. You can choose a bin width based on where the data are distributed (so that the shape of the data is clear), or to organize the data in a logical way (such as by 10s or 5s).

Hint:

Can you:

  • Explain what a histogram is?
  • Make a histogram?
  • Describe the type of data that a histogram is most useful for representing?
  • Compare line plots and histograms?

Reflect on Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use this sentence starter below if you find it to be helpful:

The most important thing I learned about histograms is ...