Reviewing How Data Affects A Histogram

Reviewing How Data Affects A Histogram

The Effect of Adjusting Bin Widths

Opening

The Effect of Adjusting Bin Widths

Look at the histogram of scores from a quiz worth 60 points. With a partner, discuss the following questions:

  • What do you think will happen if you change the bin width?
  • Why would a smaller or larger bin width be helpful?

Math Mission

Opening

Investigate how changes to data values and bin widths affect the shape of a histogram.

Explore Histogram Bin Widths

Work Time

Explore Histogram Bin Widths

Explore making histograms with the Histogram interactive by playing with a set of data and bin sizes. You can make the bins wider or narrower, and you can add or remove data from the table.

  • Create a set of data so that the histogram has an empty bin (and/or adjust the bin width to create an empty bin).
  • Enter your data about a sixth grade student. Adjust the bin width to see how the histogram changes.
  • What happens if you make the bin width 1?
  • What happens if you make the bin width equal to the range of your line plot?
  • Make a set of data with an outlier giving you more than one empty bin on the histogram. Now adjust the bin width to "hide" the outlier.

INTERACTIVE: Histogram

Hint:

  • Can you move the data points but keep the number of points in each interval the same?
  • Can you adjust the bin width?

Prepare a Presentation

Work Time

Prepare a Presentation

  • Discuss how you made each histogram so that it satisfied the conditions in the questions.
  • Explain what happened to your histogram of sixth grade student data when you changed the bin width.

Challenge Problem

  • If the range of a data set is 500, and the data set includes thousands of data points, what do you think a good bin width would be for a histogram representing the data?
  • Explain why you think the bin width you chose would be a good fit for the data.

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:

  • Can you explain how you made your histogram for that question?
  • Which histograms did you have more difficulty making? Which were easier to make?
  • How did changing the bin width in the histogram of your sixth grade student data change the histogram?

The Importance of Bin Width

Formative Assessment

Summary of the Math: The Importance of Bin Width

Write a summary of what you learned about bin width and histograms.

Hint:

Check your summary:

  • Does your summary explain how the choice of bin width can highlight or hide the shape of the data?
  • Does your summary discuss how considering the spread and shape of a data set can help you choose a bin width?

Reflect on Your Work

Work Time

Reflection

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

When I look at a histogram, I can tell these things about the data …