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

Lesson 2.22.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can make and read a histogram to display data in intervals, explain why the method works, and use it on a problem I have not seen before.

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 2.22.2 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 histogram to display data in intervals, explain why the method works, and use it on a problem I have not seen before.

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. 2Complete each step, then write the final answer.
    0481216202428323640Laps run
    30 is the first value of 30–39.

    Nine students ran 4, 9, 10, 10, 15, 19, 20, 24 and 30 laps. Use intervals of 0–9, 10–19, 20–29 and 30–39. Find each frequency.

    1. 1Which values sit on an interval edge?
    2. 2What is the frequency of 10–19?
    3. 3What are the frequencies of 20–29 and 30–39?
    4. 4Add all four frequencies. What is the total?
    Final answer:
  2. 3Complete each step, then write the final answer.
    0246860708090100Quiz scoreNumber of students

    A histogram shows 20 quiz scores. 60–69 has 3 students, 70–79 has 7, 80–89 has 6 and 90–99 has 4. How many students scored less than 80?

    1. 1Which bars show scores less than 80?
    2. 2How many students scored less than 80?
    3. 3Why can you not tell the highest score from the histogram?
    Final answer:
  3. 4Complete 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:
  4. 5Complete each step, then write the final answer.

    A histogram shows 30 players' points per game. 0–9 has 6 players, 10–19 has 11, 20–29 is missing and 30–39 has 4. What is the frequency of 20–29?

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.
    024681005101520Minutes waitedNumber of people

    A histogram shows how many minutes 25 people waited for a bus. 0–4 has 9 people, 5–9 has 8, 10–14 has 5 and 15–19 has 3. How many people waited at least 5 minutes?

    Show your work
    Final answer:

Explain your thinkingThe same data can make a histogram with intervals of 5 or of 10. Which one tells you more? Defend your choice.

ChallengeWrite your own problem

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

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