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

Lesson 2.4Represent and Describe Data in a Box Plot

Set B · Version ASecond form · supported 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.

Why This Matters The basketball league wants to compare scoring across teams. Here are the points scored by each player on the Wildcats in their last game: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. The league needs a quick visual that shows the spread, the middle 50%, and any high or low scorers. Time to build a box plot!

RememberRepresent and Describe Data in a Box Plot

Box Plots & 5-Number Summary. Formula: IQR = Q3 − Q1 A box plot is a simple picture that shows how a set of data is spread out, using just five key numbers: the lowest value, the first quartile (Q1), the median (middle), the third quartile (Q3), and the highest value.

  1. 5-Number Summary: Minimum, Lower Quartile (Q1), Median (Q2), Upper Quartile (Q3), Maximum.
  2. Draw the Box: The box spans from Q1 to Q3 and contains the middle 50% of data.
  3. Whiskers: Draw lines from the box out to the minimum and maximum

Words: Box Plot (Diagrama de caja)Median (Mediana)Quartile (Cuartil)Interquartile Range (Rango intercuartílico)Data distribution (Distribución de datos)

  1. 1Circle the letter of the best answer. Show how you know.

    The values 4, 6, 9, 12 and 19 are already in order. What is the median?

    1. A6
    2. B9
    3. C10
    4. D12
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  2. 2Circle the letter of the best answer. Show how you know.

    Order these values from least to greatest: 6, 13, 4, 9 and 3. What is the median?

    1. A4
    2. B6
    3. C7
    4. D13
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  3. 3Circle the letter of the best answer. Show how you know.

    Find the median of 4, 8, 6, 10.

    1. A6
    2. B7
    3. C8
    4. D28
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  4. 4Circle the letter of the best answer. Show how you know.

    Why must you put the values in order before finding the median?

    1. AThe median is the middle value in order
    2. BIt makes them easier to add
    3. CSo the mean can be found
    4. DOrder does not matter
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    Two basketball teams' scoring data are displayed as box plots. Team A: Min=40, Q1=52, Median=60, Q3=68, Max=75. Team B: Min=35, Q1=55, Median=61, Q3=65, Max=80. A fan says Team B is better because they scored 80 points once. What is Team A's IQR?

    1. A10
    2. B16
    3. C35
    4. D60
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  6. 6Circle the letter of the best answer. Show how you know.

    Two basketball teams' scoring data are displayed as box plots. Team A: Min=40, Q1=52, Median=60, Q3=68, Max=75. Team B: Min=35, Q1=55, Median=61, Q3=65, Max=80. A fan says Team B is better because they scored 80 points once. What is Team B's IQR?

    1. A10
    2. B16
    3. C45
    4. D61
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.

Explain your thinkingThe IQR is Q3 − Q1 = 26 − 10 = 16. What does this tell you about the middle 50% of scorers?

Sentence starter The middle 50% of players scored between ___ and ___ points. The IQR of ___ means the middle half of the data is spread across ___ points. This tells me ___.

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 2.4Represent and Describe Data in a Box Plot

Set B · Version BSecond form · core 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.

Why This Matters The basketball league wants to compare scoring across teams. Here are the points scored by each player on the Wildcats in their last game: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. The league needs a quick visual that shows the spread, the middle 50%, and any high or low scorers. Time to build a box plot!

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each team's ordered scores to its five-number summary (min, Q1, median, Q3, max).

    1. Hawks: 5, 8, 11, 15, 18, 21, 27
    2. Comets: 10, 13, 16, 20, 24, 28, 33
    3. Jets: 2, 6, 9, 14, 19, 23, 30
    4. Suns: 4, 7, 10, 16, 22, 25, 31
    • AMin 5, Q1 8, Median 15, Q3 21, Max 27
    • BMin 10, Q1 13, Median 20, Q3 28, Max 33
    • CMin 2, Q1 6, Median 14, Q3 23, Max 30
    • DMin 4, Q1 7, Median 16, Q3 25, Max 31
  2. 2Write the name of the correct group on each line.

    Each card describes a part of the stadium box plot. Sort each card under the matching box plot part.

    Groups: Part of the five-number summary Measure of spread
    • The minimum — the lowest score
    • Q1 — the median of the lower half
    • The median — the middle score
    • Q3 — the median of the upper half
    • The maximum — the highest score
    • IQR — Q3 minus Q1
    • Range — maximum minus minimum
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Two basketball teams' scoring data are displayed as box plots. Team A: Min=40, Q1=52, Median=60, Q3=68, Max=75. Team B: Min=35, Q1=55, Median=61, Q3=65, Max=80. A fan says Team B is better because they scored 80 points once. Is the fan right that Team B is better because of the 80-point game?

    1. AYes — 80 is the highest score in the data
    2. BNo — Team A's maximum is higher
    3. CYes — the maximum always decides
    4. DNo — one high game is a single extreme value, not typical performance
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    The Hawks' points per quarter are 2, 4, 5, 7, 8, 10, 12. Resting on the scoreboard, what are the minimum, median, and maximum?

    1. AMinimum 0, median 7, maximum 12
    2. BMinimum 2, median 7, maximum 12
    3. CMinimum 2, median 5, maximum 12
    4. DMinimum 2, median 8, maximum 10
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The Comets scored 6, 10, 14, 18, 22, 26, 30, 34 across 8 games. After ordering, what are Q1 and Q3?

    1. AQ1 = 12, Q3 = 28
    2. BQ1 = 10, Q3 = 30
    3. CQ1 = 14, Q3 = 26
    4. DQ1 = 20, Q3 = 34
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A box plot for the Rockets shows Min = 8, Q1 = 15, Median = 22, Q3 = 30, Max = 38. The middle 50% of their scores falls between which two values?

    1. ABetween 8 and 38
    2. BBetween 8 and 22
    3. CBetween 15 and 30
    4. DBetween 22 and 38
    Show your work

Explain your thinkingThe IQR is Q3 − Q1 = 26 − 10 = 16. What does this tell you about the middle 50% of scorers?

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