👩‍🏫 Teacher’s Guide

Objective
Students will learn and practice What Is a Box Plot? by creating and interpreting box plots using the five-number summary, IQR, whiskers, and outlier rules.

Teaching Notes

• Introduce box plots as a visual summary of spread.
• Connect to real data sets students know.

🧒 Student Worksheet

Concept and Helping Material

A box plot (box-and-whisker plot) is a graph that summarizes a data set using quartiles and extremes.

This level focuses on: What Is a Box Plot?.

Math Vocabulary and Definition

• — data that is not symmetric; one side stretches longer
• — the spread of the middle 50%: IQR = Q3 − Q1
• — a graph that shows how data is spread using a box and whiskers
• — a box plot where outliers are plotted separately and whiskers stop at non-outliers
• — a value that divides ordered data into four parts

Math Practics

1. What information does a box plot show?
2. What are the main parts of a box plot?
3. True/False: A box plot summarizes data using quartiles.
4. True/False: A box plot summarizes data using quartiles.
5. True/False: A box plot summarizes data using quartiles.
6. True/False: A box plot summarizes data using quartiles.
7. True/False: A box plot summarizes data using quartiles.
8. True/False: A box plot summarizes data using quartiles.
9. True/False: A box plot summarizes data using quartiles.
10. True/False: A box plot summarizes data using quartiles.
11. True/False: A box plot summarizes data using quartiles.
12. True/False: A box plot summarizes data using quartiles.
13. True/False: A box plot summarizes data using quartiles.
14. True/False: A box plot summarizes data using quartiles.
15. True/False: A box plot summarizes data using quartiles.
16. True/False: A box plot summarizes data using quartiles.
17. True/False: A box plot summarizes data using quartiles.
18. True/False: A box plot summarizes data using quartiles.
19. True/False: A box plot summarizes data using quartiles.
20. True/False: A box plot summarizes data using quartiles.

Math Game

Reflection

• How did you avoid common box-plot mistakes?

Guided extension: Box Plots

Use after the core lesson. These questions revisit the topic as a whole; later skills can be assigned as an extension after their prerequisites.

Key idea

Order the data before finding the median and quartiles. Here, exclude the overall median from each half when the number of values is odd. A standard box plot uses the minimum and maximum as whiskers; modified plots apply a separate outlier rule.

Worked example

For 2, 4, 6, 8, 10, 12, 14, 16: median=(8+10)/2=9, Q1=(4+6)/2=5, Q3=(12+14)/2=13, and IQR=8.

Explain and apply

1. Find the five-number summary of 1, 3, 5, 7, 9, 11, 13, 15.
2. For Q1=4 and Q3=12, find IQR.
3. Using the 1.5 IQR extension rule with Q1=4 and Q3=12, is 25 an outlier?
4. Two box plots have the same median but IQRs 3 and 9. Which has a more tightly clustered middle half?

Teacher check

Ask students to show the setup, name any domain or unit restrictions, and explain a check of their answer. For extra support, complete the worked example together before revealing answers.

Source note

Source skill reference: Everything You Need to Ace Math in One Big.pdf, PDF pages 391-394. New examples and questions use original wording and values. The 1.5 IQR outlier question is an original extension of the quartile work.