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

Lesson 2.2Represent and Describe Data in a Histogram

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 histogram to display data in intervals.

Why This Matters The basketball league has 30 players and wants to display everyone's points-per-game average in a way that shows how the data is distributed. The raw averages are: 2, 5, 7, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 32. Listing all 30 numbers is hard to read — a histogram will reveal the pattern!

RememberRepresent and Describe Data in a Histogram

Histograms & Frequency Distributions A histogram is a bar graph that groups numbers into equal ranges called intervals. The height of each bar is the frequency: how many values fall in that interval. The bars touch because the intervals are continuous.

  1. Set equal intervals along the horizontal axis with no gaps.
  2. Count the frequency (how many data values fall into each interval).
  3. Draw adjacent bars with heights equal to frequency

Words: Histogram (Histograma)Frequency (Frecuencia)Interval (Intervalo)Distribution (Distribución)Variability (Variabilidad)

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

    Match each word to what it means on a histogram.

    1. Frequency
    2. Interval
    3. Bars touch
    • AHow many values are in an interval (the bar height)
    • BAn equal-width range like 10–19
    • CWhy a histogram has no gaps between bars

    Hint Three vocab cards: one is a count, one is a range of values, and one explains the histogram's no-gap look.

Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Which of these is a statistical question?

    1. AHow many minutes are in one hour?
    2. BHow many days are in September?
    3. CHow many sides does a hexagon have?
    4. DHow many minutes did each student read last night?
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    'How tall is our flagpole?' is NOT a statistical question. Why not?

    1. AIt is about height
    2. BIt uses numbers
    3. CIt has only one answer, so there is no variability
    4. DIt is only asked once
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    A class collects this data on pets owned: 0, 2, 1, 0, 3. Which statistical question could these answers come from?

    1. AHow many students are in the class?
    2. BWhat is the largest number of pets allowed?
    3. CHow many pets are in the store?
    4. DHow many pets does each student own?
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Counting Mistake

    1. 1Data (points per game)3, 7, 11, 13, 16, 22
    2. 2Intervals0–9, 10–19, 20–29
    3. 3Frequency count0–9: 2, 10–19: 2, 20–29: 1
    4. 4ConclusionSo the histogram bars have heights 2, 2, and 1.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Count the data values first: 3, 7, 11, 13, 16, 22 is 6 values, but the frequencies add to only 5. A value was missed.

    Correct work
    Correct answer:
  2. 6Find the mistake. Explain it, then show the correct work.

    Spot the Interval Mistake

    1. 1Data (assists per game)1, 4, 6, 9, 12, 15, 18
    2. 2Intervals the student chose0–5, 6–10, 12–18
    3. 3Frequency count0–5: 2, 6–10: 2, 12–18: 3
    4. 4ConclusionThe student drew three bars and said the histogram was complete.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Check the width of each interval the student used. Are 0–5, 6–10, and 12–18 all the same size?

    Correct work
    Correct answer:

Explain your thinkingThe tallest bar is the 10–19 interval with 16 players. What does the shape of this histogram tell you about scoring in the league?

Sentence starter Most players score between ___ and ___ points per game. The histogram is skewed ___ because ___. This tells me that ___.

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 2.2Represent and Describe Data in a Histogram

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 histogram to display data in intervals.

Why This Matters The basketball league has 30 players and wants to display everyone's points-per-game average in a way that shows how the data is distributed. The raw averages are: 2, 5, 7, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 32. Listing all 30 numbers is hard to read — a histogram will reveal the pattern!

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Drag each player's points-per-game value into the correct interval bin (each bin is 10 wide).

    Groups: 0–9 points 10–19 points 20–29 points
    • 6 points
    • 8 points
    • 13 points
    • 17 points
    • 21 points
    • 25 points
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A soccer coach looks at a histogram of shots-per-game for the team: 0–2 shots: 1 player, 3–5 shots: 8 players, 6–8 shots: 10 players, 9–11 shots: 3 players, 12–14 shots: 1 player. The coach says, 'Most of my players take a good number of shots.' Which interval has the most players?

    1. A0–2 shots
    2. B3–5 shots
    3. C6–8 shots
    4. D9–11 shots
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    A soccer coach looks at a histogram of shots-per-game for the team: 0–2 shots: 1 player, 3–5 shots: 8 players, 6–8 shots: 10 players, 9–11 shots: 3 players, 12–14 shots: 1 player. The coach says, 'Most of my players take a good number of shots.' How many players take between 3 and 8 shots per game?

    1. A8
    2. B10
    3. C18
    4. D23
    per 1
  3. 4Circle the letter of the best answer. Show how you know.

    A soccer coach looks at a histogram of shots-per-game for the team: 0–2 shots: 1 player, 3–5 shots: 8 players, 6–8 shots: 10 players, 9–11 shots: 3 players, 12–14 shots: 1 player. The coach says, 'Most of my players take a good number of shots.' Does the histogram support the coach's claim?

    1. ANo — most players take 0–2 shots
    2. BNo — the data is skewed right
    3. CYes — 18 of 23 players cluster in the middle intervals
    4. DYou cannot tell from a histogram
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Data: 4, 8, 9, 12, 14, 15, 17, 18, 19, 22, 24, 27, 31, 33. How many values fall in the 10–19 interval?

    1. A3
    2. B5
    3. C6
    4. D9
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    Frequencies: 0–9: 3, 10–19: 9, 20–29: 5, 30–39: 2. Which interval has the tallest bar?

    1. A0–9 with 3 players
    2. B10–19 with 9 players
    3. C20–29 with 5 players
    4. D30–39 with 2 players
    Show your work

Explain your thinkingThe tallest bar is the 10–19 interval with 16 players. What does the shape of this histogram tell you about scoring in the league?

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