Manipulating Data Points

Manipulating Data Points

Introduction to Making Box Plots With Line Plots

Opening

Introduction to Making Box Plots With Line Plots

This line plot and box plot represent the same data:

{0, 7, 13, 20}

  1. Why doesn't the size of the box on the box plot line up with the data underneath it on the line plot?
  2. What would happen to the "whiskers" if you changed the value of the lower or upper extreme values?
  3. How are the box plot and line plot related?

Math Mission

Opening

Create data sets with box plots that satisfy given criteria.

Explore Making Box Plots With Line Plots

Work Time

Explore Making Box Plots With Line Plots

Explore making box plots when adding data to a line plot. Play with the data points and see what happens.

  • Try to make a box plot for each of the following criteria:
    • The box is very narrow and the whiskers are long
    • The box is wide and the whiskers are short
    • The median is to the far right or far left of the box
    • One whisker is short and the other is long
    • The box plot is symmetrical
    • The interquartile range is 10
    • The median is 6
    • The upper quartile is 16

INTERACTIVE: Box Plot

Hint:

Think about a data set with 12 values.

  • The box represents the middle 6 values. If the box is narrow, what do you know about these values?
  • The left whisker represents the least 3 values. If the left whisker is long, what do you know about these values?
  • The right whisker represents the greatest 3 values. If the left whisker is long, what do you know about these values?
  • List 12 data values that you think will meet the criteria and use the Box Plot interactive to test them.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain why each box plot represents the given criteria.
  • Describe the process you used to create box plots that meet the given criteria.

Challenge Problem

  • Can you re-create any of the box plots you just constructed using different sets of data?

INTERACTIVE: Box Plot

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes as your classmates present their box plots.

Hint:

As your classmates present, ask questions such as:

  • Can you explain how you created your box plot for that question?
  • Which box plots did you have more difficulty creating?
  • Which box plots were easier to create?
  • What do you think it means when one whisker is short and the other is long?

About Box Plots

Formative Assessment

Summary of the Math: About Box Plots

Read and Discuss

  • A box plot shows how data are spread. It does not show individual values like a line plot does. It is possible to create many different data sets with the same box plot.
  • For example, once you make a box plot, you can add the same number of data points to each quartile and the plot will not change.
  • You can see the median in a box plot, but you cannot tell what the other measures of center are like you can in a line plot.

Hint:

Can you:

  • Discuss the characteristics of a box plot?
  • Discuss the similarities and differences between the information a line plot shows and the information a box plot shows?

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.

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