Calculating The Five-Number Summary & Interquartile Range (IQR)

Calculating The Five-Number Summary & Interquartile Range (IQR)

Introduction to Box Plots

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Introduction to Box Plots

This image shows a box-and-whisker plot (or just a box plot).

Discuss the following information with your partner.

  • To draw a box plot you need to know five numbers, called the five-number summary:
    1. Lower extreme: The least value in the set of data
    2. Lower quartile: The middle of the lower half of the data
    3. Median: The middle value
    4. Upper quartile: The middle of the upper half of the data
    5. Upper extreme: The greatest value in the set of data
  • The box part of a box plot shows the spread of the middle 50 percent of the data. The length of the box is called the interquartile range and represents the distance between the upper and lower quartiles.

Quiz Scores

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Quiz Scores

These are the quiz score data used in Lesson 4:

{0, 1, 1, 2, 2, 3, 3, 3, 4, 5, 6, 6}

Discuss how the five-number summary is represented in a box plot.

  • The five-number summary for this data:
    • Lower extreme: 0
    • Lower quartile: 1.5 (because the middle pair of values for the lower half of the data is 1 and 2, and 1.5 is halfway between 1 and 2—{0,1,1,2,2,3})
    • Median: 3 (because the two middle numbers are both 3)
    • Upper quartile: 4.5 (because the middle pair of values for the upper half of the data is 4 and 5, and 4.5 is halfway between 4 and 5—{3,3,4,5,6,6})
    • Upper extreme: 6
  • Study the box plot below. Explain to a partner how the five-number summary was used to draw the box plot.

Math Mission

Opening

Construct a box plot to show the spread of your data about a sixth grade student.

Create a Box Plot of My Data

Work Time

Create a Box Plot of My Data

Find your work about a typical sixth grade student from the lesson "Describe a Sixth Grade Student". Copy your line plot from Lesson 7, Task 3, into your notebook.

  • Find the five-number summary for your data.
  • Draw the box plot directly above your line plot.
  • On your box plot, label the lower and upper extremes, the lower and upper quartiles, the median, and the interquartile range (also called IQR).

INTERACTIVE: Line Plot with Stats

Hint:

Follow these steps to draw a box plot:

  • Calculate the numbers in the five-number summary.
  • Draw a box from the lower quartile to the upper quartile (this is the interquartile range, or IQR).
  • Draw a line segment from the left side of the box to the lower extreme of the range, and a line segment from the right side of the box to the upper extreme of the range.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Give the five-number summary for your data.
  • Show the lower and upper extremes, the lower and upper quartiles, the median, and the interquartile range.
  • Explain what your box plot shows about the data.
  • Show how the box plot relates to the line plot.

Challenge Problem

  • If there are 32 data values in a set of data, how many values will be in the interquartile range?

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:

  • How did you find the numbers in your five-number summary?
  • How did you figure out where to draw the box?
  • How did you find the interquartile range of your data?
  • What does your box plot tell you about your data?

All About Box Plots

Formative Assessment

Summary of the Math: All About Box Plots

Write a summary of what you learned about box plots.

Hint:

Check your summary.

  • Do you describe a box plot and what it shows about a set of data?
  • Do you describe each measure in the five-number summary?
  • Do you describe the interquartile range?

Reflect on Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use these sentence starters below if you find them to be helpful.

Box plots are similar to line plots in the following ways …

Box plots are different from line plots in the following ways …