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

Lesson 2.2Describing Histogram Shape

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 side by side: 0-9 pts (3 players), 10-19 pts (8 players), 20-29 pts (4 players)
FrequencySpanish: Frecuencia How many times a value shows up. Bar height shows the count
IntervalSpanish: Intervalo A range of numbers used to group data. 0-9, 10-19, 20-29 are intervals of width 10 — each covers 10 values
DistributionSpanish: Distribución How the data is spread out. Most values near the peak
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 means three values are between 10 and 19.

How it worksWorked examplereading the shape of a histogram

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

A histogram has a bar of height 2 over 60-69, height 4 over 70-79, and height 2 over 80-89.

  1. Sketch the bars at heights 2, 4, and 2 over the three intervals, touching with no gaps.
  2. Find the peak: the tallest bar covers the interval 70-79.
  3. Compare sides: the bar left of the peak and the bar right of it are the same height.
  4. Matching sides mean the data is nearly symmetric around the peak.

Answer: The histogram peaks over 70-79 and is symmetric, so a typical value falls in 70-79.

Now you trySame steps, your turn

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

A histogram has bars of height 1 over 400-409, height 4 over 410-419, height 3 over 420-429, and height 1 over 430-439.

  1. Sketch the four touching bars at the heights listed above.
  2. The peak covers the interval - .
  3. Bars left of the peak: Bars right of the peak: Do they match?
  4. The shape is (symmetric / not symmetric) because .
Answer:peak interval and shape

Say it and write itSentence starters

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

  • The peak of this histogram is the interval .
  • Most of the values land between and .
  • The shape is because the left side the right side.
  • A typical value falls in the interval .

Word bank histogrampeakshapesymmetricintervalfrequencytypicalspreaddistributiontallestcompareside

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 2.2Describing Histogram Shape

Apply Day · 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.

  1. 1Complete each step, then write the final answer.

    Data: 1, 4, 12, 13, 17, 25. Use intervals of 0–9, 10–19 and 20–29. What is the frequency of 0–9?

    Show your work

    Hint Count the values from 0 to 9.

    Final answer:
  2. 2Complete each step, then write the final answer.
    0123450102030Data valuesFrequency

    A histogram has bars 0–9: 5, 10–19: 2 and 20–29: 3. How many values are there in all?

    Show your work

    Hint Each bar height is a count. Add the heights.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Data: 7, 15, 21, 22, 26, 28. Use intervals of 0–9, 10–19 and 20–29. What is the frequency of 20–29?

    Show your work

    Hint Count the values from 20 to 29.

    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 2.2Describing Histogram Shape

Apply Day · 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.

  1. 1Complete each step, then write the final answer.

    Kim makes a histogram of 4, 10, 15, 19, 20, 27. She says the 10–19 bar has a height of 4. She counted 10, 15, 19 and 20. What is the correct height?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Data: 19, 20, 20, 21, 29, 30, 38. Use intervals of 10–19, 20–29 and 30–39. What is the frequency of 20–29?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Data: 6, 7, 11, 18, 24, 25, 29. Use intervals of 0–9, 10–19 and 20–29. What is the frequency of 20–29?

    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 2.2Describing Histogram Shape

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

    A histogram has bars 0–9: 4, 10–19: 6 and 20–29: 2. Which statement must be true?

    1. A6 values are from 10 to 19.
    2. BOne value is exactly 15.
    3. CThe greatest value is 29.
    4. DThe data has only 3 values.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A histogram uses intervals 0–9, 10–19, 20–29, and 30–39. A data value of 19 belongs in which interval?

    1. A10–19
    2. B0–9
    3. C20–29
    4. DIt belongs in two intervals.
    Show your work
  2. 3Complete each step, then write the final answer.

    Data: 8, 10, 13, 19, 20, 26, 30, 30. Use intervals of 0–9, 10–19, 20–29 and 30–39. What is the frequency of 10–19?

    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