Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.4Comparing Box Plots

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can make and read a box plot to summarize a data set.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Box PlotSpanish: Diagrama de caja A graph that shows how data is spread using five key numbers. Box with two whiskers
MedianSpanish: Mediana The middle number when you put them in order. Data: 10, 15, 20, 25, 30 → median is 20 (the 3rd value)
QuartileSpanish: Cuartil Numbers that split the data into four equal parts. Data: 2, 4, 6, 8, 10, 12, 14 → Q1 = 4 (median of lower half), Q3 = 12 (median of upper half)
Interquartile RangeSpanish: Rango intercuartílico The spread of the middle half of the data (Q3 − Q1). If Q1 = 12 and Q3 = 20, then IQR = 20 − 12 = 8 — the middle 50% spans 8 units
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. A box plot where the median is centered in the box shows symmetric distribution
VariabilitySpanish: Variabilidad How spread out the numbers are. Small IQR = low variability in the middle 50%. Large IQR = high variability

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Trail X: Q1 18, median 20, Q3 22. Trail Y: Q1 19, median 26, Q3 33 (minutes).

  1. Medians: 26 − 20 = 6, so Y is typically 6 min longer.
  2. Box widths: X is 22 − 18 = 4; Y is 33 − 19 = 14.

Answer: Y is longer; X is more consistent

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The median of is higher than the median of .
  • The box for is wide, so its middle half is .
  • Both groups have the same but different .
  • I would say is more consistent because .

Word bank box plotmedianquartileboxwhiskercenterspreadwidernarrowerconsistenttypicalcompare

Watch out!A common mistake

A common mistake in Display Data: Box Plots is treating a quartile as just one data point instead of the median of a half

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.4Comparing Box Plots

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can make and read a box plot to summarize a data set.

  1. 1Complete each step, then write the final answer.

    Here are 5 values in order: 1, 4, 6, 9, 10. What is Q1?

    Show your work

    Hint The median is 6. The lower half is 1 and 4.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Here are 7 values in order: 2, 4, 5, 8, 11, 12, 15. What is Q3?

    Show your work

    Hint The median is the 4th value. Q3 is the middle of the 3 values after it.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Here are 9 values in order: 1, 2, 5, 6, 8, 9, 10, 13, 14. What is Q1?

    Show your work

    Hint The median is the 5th value. The lower half has 4 values.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.4Comparing Box Plots

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can make and read a box plot to summarize a data set.

  1. 1Complete each step, then write the final answer.

    A box plot shows least 2, Q1 5, median 8, Q3 12, greatest 15. Ava says the box ends at the greatest value. At what number does the box really end on the right?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Here are 7 values in order: 1.5, 2, 3.5, 4, 5, 6.5, 8. What is Q3?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Here are 9 values in order: 3, 4, 6, 7, 9, 11, 12, 14, 16. What is Q1?

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.4Comparing Box Plots

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can make and read a box plot to summarize a data set.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Team A's box plot has Q1 20 and Q3 30. Team B's has Q1 15 and Q3 40. Each team has 20 players. Which statement is true?

    1. ABoth boxes hold about 10 players.
    2. BTeam B's box holds more players because it is wider.
    3. CTeam A's box holds more players because it is shorter.
    4. DYou cannot tell how many players are in either box.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A box plot has a 5-number summary of minimum 4, Q1 = 8, median 12, Q3 = 18, maximum 24. What is the interquartile range?

    1. A6
    2. B10
    3. C12
    4. D20
    Put the data in order
    Work
  2. 3Complete each step, then write the final answer.

    Here are 8 values in order: 6, 8, 9, 11, 14, 16, 17, 22. What is Q1?

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help