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 examplecomparing two groups from their box plots

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

Group A: min 40, Q1 47, median 53, Q3 59, max 66. Group B: min 44, Q1 51, median 57, Q3 62, max 71.

  1. Compare the medians first: Group A sits at 53 and Group B sits at 57.
  2. The group with the higher median has the higher typical value.
  3. Compare the boxes: A runs from 47 to 59, and B runs from 51 to 62.
  4. A narrower box means the middle half of that group is packed more tightly.

Answer: Group B is typically higher (median 57) and its box is slightly narrower, so it is a bit tighter.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Class P: min 12, Q1 19, median 26, Q3 31, max 38. Class Q: min 15, Q1 17, median 22, Q3 35, max 39.

  1. Medians: P Q Which is higher?
  2. Boxes: P runs to . Q runs to .
  3. Which box is wider? What does that say about the middle half?
  4. One sentence comparing center and spread:
Answer:comparison of center and spread

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 outA 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 — for the lower half 4, 8, 10, 14, some students pick 10 (the last value) as Q1 instead of finding the median of that half: Q1 = (8 + 10) ÷ 2 = 9. A second common slip is finding IQR by adding the quartiles instead of subtracting, writing IQR = Q3 + Q1 (like 30 + 18 = 48) instead of IQR = Q3 − Q1 (30 − 18 = 12) — always order the data first, then subtract Q1 from Q3 to find the spread of the middle 50%.

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:
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:
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:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help