Grade 6 Math · Topic 70

Histograms

A histogram shows the frequency of data grouped into equal-width intervals (called bins). It is perfect for large numerical data sets where individual dots would be cluttered.

Lesson alignment: 6.SP.B.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Build a histogram

Group the data into equal-width intervals and compare their frequencies.

Think first: Which interval do you expect to have the most values?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

A histogram of ages has bins 0--9, 10--19, 20--29, 30--39 with heights 5, 12, 8, 3. How many people total?

Start by writing the calculation clearly: 5 + 12 + 8 + 3 = 28 people.

Answer: 28

Worked example 2

Which interval contains the most people, and how many?

The 10--19 bin has 12 people, the tallest bar.

Answer: 10--19 with 12

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. Total in survey =
    Check

    32

  2. Modal interval =
    Check

    20--29

  3. Frequency for 20-29 =
    Check

    11

  4. Number under 20 =
    Check

    13

  5. Number at least 30 =
    Check

    8

  6. Number of bins =
    Check

    5

  7. Width of each bin =
    Check

    10

  8. Difference between tallest and shortest bar =
    Check

    9

Try this situation 1

A histogram of test scores has bins 60--69, 70--79, 80--89, 90--99 with frequencies 3, 8, 10, 5. How many students took the test?

Show a worked solution

Answer: 26 students.

Start by writing the calculation clearly: 3 + 8 + 10 + 5 = 26.

Try this situation 2

Using the same histogram, how many students scored at least 80?

Show a worked solution

Answer: 15 students.

Start by writing the calculation clearly: 10 + 5 = 15 (the 80--89 and 90--99 bars).

Fresh questions · saved on this device

Practice this skill

11 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A histogram has frequencies 3 for 0–9, 5 for 10–19, and 2 for 20–29. Which interval contains 14?

2. A histogram bar for 15–19 has height 7. What does the 7 represent?

3. Three histogram intervals have frequencies 4, 6, and 3. How many data values are shown altogether?

4. A histogram has bar heights 2, 8, 5, and 3. Which interval is the modal interval?

5. A histogram groups quiz scores into intervals. What does the horizontal axis usually show?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Statistics & Data quiz ↗Try a full practice test ↗