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

Lesson 2.2Represent and Describe Data in a Histogram

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can make and read a histogram to display data in intervals.

Start hereWords for this lesson

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

WordWhat it meansExample
HistogramSpanish: Histograma A bar graph that groups data into equal ranges. The bars touch. Bars that touch
FrequencySpanish: Frecuencia How many times a value shows up. Bar height shows the count
IntervalSpanish: Intervalo A range of numbers used to group data. 10-19 is one interval
DistributionSpanish: Distribución How the data is spread out. Tallest bar in the middle
VariabilitySpanish: Variabilidad How spread out the numbers are. Data in just 2 intervals = low variability. Data across 6 intervals = high variability
Frequency tableSpanish: Tabla de frecuencias A table that lists each interval and how many values fall in it. 10-19 . . . 3

How it worksWorked examplegrouping data into a frequency table

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

Seven plants grew these heights in cm: 61, 74, 88, 76, 63, 71, 79. Use ten-unit intervals.

  1. Choose equal intervals that cover the data with no gaps: 60-69, 70-79, 80-89.
  2. Tally each value into exactly one interval. 61 and 63 both land in 60-69.
  3. Count each interval. 60-69 holds two plants, 70-79 holds four, 80-89 holds one.
  4. Draw touching bars at those heights above the three interval labels.

Answer: The frequency table reads 60-69: 2, 70-79: 4, 80-89: 1, and the tallest bar is 70-79.

Now you trySame steps, your turn

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

Seven phone batteries held these charges: 34, 47, 31, 42, 38, 44, 49. Use ten-unit intervals.

  1. Write intervals that cover the data with no gaps: - and -
  2. Tally each value into exactly one interval, crossing it off as you go.
  3. Frequency of the lower interval: Frequency of the upper interval:
  4. Sketch two touching bars whose heights match those two counts.
Answer:frequency of each interval

Say it and write itSentence starters

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

  • My intervals are wide and they do not .
  • The interval holds values.
  • The tallest bar is because .
  • The bars touch because the intervals .

Word bank histogramintervalfrequencytallyequaloverlapbarheightcounttouchdistributiondata

Watch outA common mistake

A common mistake in Display Data: Histograms is counting a boundary value in two intervals at once — for example, putting the value 10 in both the '0–9' bin and the '10–19' bin. Each data value belongs to exactly ONE interval. Before you submit, add up all your frequencies and check that the total matches the number of data values you started with.

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

Lesson 2.2Represent and Describe Data in a Histogram

Version ASupported 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.

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

    In a histogram, what does the height of each bar represent?

    1. AThe frequency (count) of data in that interval
    2. BThe average of the data in that interval
    3. CThe range of the interval
    4. DThe median of the data

    Hint Think about what you'd count to draw one bar: you'd tally how many data values land inside that interval.

    Show your work
  2. 2Write the name of the correct group on each line.

    Order the steps for making a histogram.

    Groups: Steps (in order)
    • Step 1: Choose equal-sized intervals that cover all the data
    • Step 2: Count how many data values fall in each interval (frequency)
    • Step 3: Draw bars for each interval — height = frequency
    • Step 4: Make sure bars touch with no gaps

    Hint You must decide on intervals before counting data in each one.

  3. 3Circle the letter of the best answer. Show how you know.

    A histogram bar for the interval 20–29 reaches a height of 7. What does the 7 tell you?

    1. AThe largest value is 7
    2. BThere are 7 intervals
    3. CThe interval is 7 wide
    4. D7 data values fall between 20 and 29

    Hint Two numbers appear here: the interval (20–29) and the height (7). Keep straight which one is a range and which is a count.

    Show your work
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?

    1. A12
    2. B15
    3. C20
    4. D28

    Hint The question asks for the TOTAL across all four intervals — not the tallest bar and not the biggest interval.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 5Circle the letter of the best answer. Show how you know.

    How is a histogram different from a regular bar graph?

    1. AHistogram bars touch (no gaps) because the intervals are continuous ranges
    2. BThere is no difference
    3. CHistograms use colors and bar graphs don't
    4. DBar graphs show numbers and histograms show words

    Hint Picture both graphs side by side: one has spaces between its bars, one doesn't. Ask why that would be.

    Show your work
  3. 6Circle the letter of the best answer. Show how you know.

    A histogram has intervals: 0–4, 5–9, 10–14, 15–19. What is the width of each interval?

    1. A4
    2. B5
    3. C10
    4. D19

    Hint Width means how many whole-number values fit inside one interval — count them, don't just subtract the endpoints.

    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?

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

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

Version BCore 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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the table.

    Interval (Yards)Frequency
    Player rushing yards per game: 0, 5, 12, 15, 18, 22, 25, 28, 31, 35, 40, 45
    0–9
    10–19
    20–29
    30–39
    40–49
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each term to its description.

    1. Histogram
    2. Bar graph
    3. Frequency
    4. Interval
    • ABars touch, shows frequency by interval
    • BBars separated, shows categories
    • CCount of values in an interval
    • DRange of values grouped together
  3. 3Write the name of the correct group on each line.

    Rank the intervals from highest to lowest frequency.

    Groups: Most to fewest players
    • 10–19: 11 players
    • 20–29: 7 players
    • 0–9: 4 players
    • 30–39: 2 players
  4. 4Complete the table. Show how you found each value.

    Use this data set of rebounds per game to complete the frequency table (intervals of 5): 1, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16.

    Interval (Rebounds)Frequency
    0–4
    5–9
    10–14
    15–19
    Show your work
Part 2Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    A histogram of test scores shows: 50–59: 2, 60–69: 5, 70–79: 10, 80–89: 8, 90–99: 3. Which interval has the most students?

    1. A60–69 with 5 students
    2. B70–79 with 10 students
    3. C80–89 with 8 students
    4. D90–99 with 3 students
    Show your work
  2. 6Circle the letter of the best answer. Show how you know.

    A histogram of goals-per-game shows: 0–1: 9 players, 2–3: 6, 4–5: 3, 6–7: 1. What shape is this distribution?

    1. APerfectly symmetric
    2. BSkewed right (most players low, tail toward high values)
    3. CFlat / uniform (all bars equal)
    4. DSkewed left (most players high, tail toward low values)
    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?

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

ChallengeExtension

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

Learning target I can make and read a histogram to display data in intervals.

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

    Match each scenario to its histogram shape.

    Groups: Symmetric (peak in the middle) Skewed Right (tail points to high values) Skewed Left (tail points to low values)
    • Player heights on a team — most are average height, fewer are very tall or very short
    • Points per game — most players score low, a few stars score very high
    • Free-throw % of experienced players — most are high, a few are very low
  2. 2Circle the letter of the best answer. Show how you know.

    Two histograms show the SAME 40 test scores — one uses intervals of 5, the other intervals of 20. Which statement is true?

    1. AThe interval-of-5 histogram has more bars and shows more detail about the shape
    2. BThe interval-of-5 histogram leaves some scores out
    3. CThe interval-of-20 histogram has more bars
    4. DBoth histograms must look exactly the same
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A histogram of points-per-game has its tallest bars on the LEFT (low scores) and a long tail stretching RIGHT toward a few high scorers. How is this distribution described?

    1. ASkewed left
    2. BSymmetric
    3. CBimodal (two equal peaks)
    4. DSkewed right
    Show your work
Part 3Explain and correctreasoning
  1. 4Find the mistake. Explain it, then show the correct work.

    Find the Histogram Error

    1. 1DataTest scores: 55, 62, 68, 70, 72, 75, 78, 80, 82, 85, 88, 90, 95
    2. 2Intervals50–59, 60–69, 70–79, 80–89, 90–100
    3. 3Frequency table50–59: 1, 60–69: 2, 70–79: 3, 80–89: 4, 90–100: 2
    4. 4ConclusionThe histogram is symmetric because the bars go 1, 2, 3, 4, 2.

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

    Correct work
    Correct answer:
  2. 5Answer in complete sentences.

    A teacher collected test scores and made two different histograms — one with intervals of 5 (50–54, 55–59, etc.) and one with intervals of 20 (50–69, 70–89, 90–109). Both use the same data. How might the two histograms look different? Which interval size gives you more detail about the distribution? When might the larger interval be better?

    Write your 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?

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