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

Lesson 2.42.4 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 2.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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. Q1, median, Q3
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.

Times (min): 14, 5, 20, 9, 23, 11, 16.

  1. Order: 5, 9, 11, 14, 16, 20, 23. Median = 14.
  2. Lower half 5, 9, 11: Q1 = 9. Upper half 16, 20, 23: Q3 = 20.
  3. Box from 9 to 20, line at 14, whiskers to 5 and 23.

Answer: 5, 9, 14, 20, 23

Now you trySame steps, your turn

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

Find the five numbers for a box plot of this data: 2, 5, 5, 8, 11.

Answer:

Say it and write itSentence starters

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

  • In order the values are .
  • The median is , so the lower half is .
  • Quartile 1 is and quartile 3 is .
  • The box stretches from to , which holds of the data.

Word bank box plotquartilemedianminimummaximumwhiskerboxorderlower halfupper halfmiddlespread

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 2.42.4 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 2.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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. 2Complete each step, then write the final answer.
    0246810121416182022Data values
    10 values: an even count.

    Find the five numbers for a box plot of this data: 4, 5, 7, 9, 10, 12, 14, 15, 18, 21. There are 10 values.

    1. 1Find the median of the 10 values.
    2. 2The lower half is 4, 5, 7, 9, 10. What is Q1?
    3. 3Find Q3, the middle of the upper half.
    4. 4What are the least and greatest values?
    Final answer:
  2. 3Complete each step, then write the final answer.
    3034384246505458626670
    Jump distances in inches

    A box plot shows the jumps of 40 students in inches: least 30, Q1 42, median 48, Q3 55, greatest 70. About how many students jumped from 42 to 55 inches?

    1. 1Which part of the box plot goes from 42 to 55?
    2. 2The box holds half the data. About how many students is that?
    3. 3About how many students jumped more than 55 inches?
    4. 4The right whisker is long. Why does it hold only about 10 students?
    Final answer:
  3. 4Complete 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:
  4. 5Complete each step, then write the final answer.

    Eight values in order are 2, 4, 6, 9, 11, ?, 16, 20. Q3 is 15. Find the missing value.

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.
    1015202530354045505560
    Video game prices in dollars

    A box plot shows the prices of 24 video games: least $10, Q1 $20, median $30, Q3 $45, greatest $60. About how many games cost $30 or less?

    Show your work
    Final answer:

Explain your thinkingIn the jump box plot, the right whisker is longer than the box. Which part holds more students? Defend your answer.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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