MathBatchSign in
Free quiz generator

Histogram Quiz Generator

Generate free printable histogram quizzes with deterministic graphs, varied real-world contexts, multiple-choice questions, and verified answer keys.

Verified answersGenerated with deterministic math
Free step-by-step lesson

Learn histograms

A histogram displays the distribution of numerical data in adjoining intervals called bins. Bar height represents frequency, while the overall pattern can reveal shape, center, spread, gaps, and unusual regions.

By the end of this lesson

You will read histogram intervals, compare bar heights, and describe a distribution.

Review first if you need it: Mean, Median, Mode
01

The idea in plain English

A histogram groups numerical values into intervals. Each bar shows how many values fall inside one interval.

The bars touch because the number intervals continue without category gaps.

02

How to recognise this kind of question

  • The horizontal axis shows number ranges rather than named categories.
  • Bars usually touch.
  • The vertical axis shows frequency or count.

Quick decision: Find the correct interval first, then read that bar's height.

03

The method

  1. Read the horizontal axis to identify each bin and its boundaries.
  2. Use bar height and the frequency scale to determine how many observations fall in each interval.
  3. Study the full pattern before describing shape, approximate center, spread, gaps, or unusual regions.
  4. Remember that grouped bars do not reveal every exact raw value.
04

Worked examples

Start here

A histogram's 20–30 bin has height 8 and its 30–40 bin has height 5.

  1. The first bar represents 8 observations from 20 up to 30.
  2. The next bar represents 5 observations from 30 up to 40.
  3. Add the frequencies when the question asks about the full 20–40 region.

Answer: 13 observations from 20 up to 40

A little harder

Bars for 0–9, 10–19, and 20–29 have heights 2, 6, and 3. Which interval is most common?

  1. Compare the three bar heights.
  2. The tallest bar has height 6.

Answer: 10–19

05

Your turn—with help

Try it

The 30–39 bar has height 7. What does that mean?

Need a hint?

Connect the interval to the bar's count.

Show the answer and steps
  1. The horizontal interval is 30–39.
  2. The vertical height is a frequency of 7.

Answer: Seven values are from 30 through 39.

06

Watch out for this mistake

Incorrect: A bar from 10–19 with height 5 means the total is 15

Why it fails: The height is a count, not a number to add to the interval boundary.

Do this instead: It means five data values fall from 10 through 19.

07

Quick check

Try these without looking. Then open each answer to check your thinking.

Question 1

A 5–9 bar has height 4. How many values are in that interval?

Need a hint?

Read the height.

Show the answer and steps
  1. The bar height is the frequency.

Answer: 4

Question 2

Which interval has the greatest frequency?

Need a hint?

Look for the tallest bar.

Show the answer and steps
  1. Compare heights, not widths.

Answer: The interval with the tallest bar

Question 3

Can a histogram identify every exact data value?

Need a hint?

Values are grouped into intervals.

Show the answer and steps
  1. The graph shows interval counts, not each original value.

Answer: No

Remember thisInterval tells where; height tells how many.

Common mistakes

  • Treating the horizontal scale as categories instead of numerical intervals.
  • Leaving gaps between histogram bars when the bins are contiguous.
  • Claiming an exact mean, median, range, or outlier from grouped data when only an estimate is supported.
  • Confusing frequency with cumulative or relative frequency.

Practice tips

  • State interval boundaries clearly, such as 20 up to but not including 30.
  • Check totals before calculating percentages or cumulative frequencies.
  • Compare a histogram's tail lengths when deciding whether it is skewed.
  • Unlike a bar graph, a histogram groups numerical values into touching intervals.

Frequency and bins

Each bin covers a numerical interval. Its bar height is the number of observations in that interval. Add neighboring bar heights for combined or cumulative counts, and divide by the total for relative frequency.

Distribution shape

A roughly mirrored pattern is approximately symmetric. A longer left tail is skewed left, while a longer right tail is skewed right. Similar bar heights across the range suggest an approximately uniform distribution.

Center and spread

A histogram supports estimates of a typical value and the represented range, but grouping usually prevents recovery of the exact raw-data mean, median, or individual outliers.

Histogram vs. bar graph

Histograms display numerical intervals in order, so adjoining bins touch. Bar graphs compare separate categories and commonly leave space between bars.

Free printable practice

Now practise what you learned.

Create a fresh set with verified answers. No signup required.

45 verified questionsSeed 482731
MMathBatch
Quiz #482731
Statistics practice

Histogram Quiz

Name Date

Refer to each histogram and answer the questions that follow. Circle the letter of the best answer.

Histogram 1Plant HeightsHeights of plants in a classroom experiment
10 up to 15: 6 observations; 15 up to 20: 16 observations; 20 up to 25: 26 observations; 25 up to 30: 20 observations; 30 up to 35: 0 observations; 35 up to 40: 8 observations; 40 up to 45: 2 observations071421281015202530354045Height (cm)Frequency

  1. 1.1. Which value is the best estimate of the distribution's center (height (cm))?

    1. 15
    2. 20
    3. 30
    4. 25

  2. 1.2. Approximately what percentage of observations fall from 20 up to but not including 30?

    1. 59%
    2. 69%
    3. 58%
    4. 64%

  3. 1.3. How many observations fall from 35 up to but not including 40?

    1. 24 observations
    2. 32 observations
    3. 8 observations
    4. 16 observations
Histogram 2Pet WeightsWeights of pets recorded at a community event
0 up to 5: 4 observations; 5 up to 10: 9 observations; 10 up to 15: 14 observations; 15 up to 20: 10 observations; 20 up to 25: 5 observations; 25 up to 30: 0 observations; 30 up to 35: 2 observations048121605101520253035Weight (lb)Frequency

  1. 2.1. Which interval may contain unusually high observations separated from the main distribution?

    1. 0–5
    2. 30–35
    3. 15–20
    4. 20–25

  2. 2.2. Which description best matches the distribution's shape?

    1. Skewed right
    2. Has a separated high region
    3. Skewed left
    4. Approximately uniform

  3. 2.3. How many observations are below 20?

    1. 57 observations
    2. 36 observations
    3. 37 observations
    4. 67 observations
Histogram 3Books ReadBooks read during a school reading challenge
0 up to 2: 4 observations; 2 up to 4: 9 observations; 4 up to 6: 14 observations; 6 up to 8: 10 observations; 8 up to 10: 5 observations; 10 up to 12: 0 observations; 12 up to 14: 2 observations048121602468101214BooksFrequency

  1. 3.1. Which interval is a gap with no observations?

    1. 10–12
    2. 0–2
    3. 8–10
    4. 12–14

  2. 3.2. Which interval may contain unusually high observations separated from the main distribution?

    1. 8–10
    2. 6–8
    3. 2–4
    4. 12–14

  3. 3.3. Which interval contains the value 3?

    1. 8–10
    2. 2–4
    3. 6–8
    4. 12–14
Histogram 4RainfallDaily rainfall amounts recorded during a season
0 up to 2: 2 observations; 2 up to 4: 4 observations; 4 up to 6: 6 observations; 6 up to 8: 10 observations; 8 up to 10: 16 observations; 10 up to 12: 22 observations; 12 up to 14: 28 observations0714212802468101214Rainfall (mm)Frequency

  1. 4.1. Which statement is directly supported by the histogram?

    1. 12–14 contains the exact mean.
    2. 12–14 contains no observations.
    3. 12–14 contains the greatest number of observations.
    4. The exact median can be read from one bar.

  2. 4.2. How many observations are below 4?

    1. 5 observations
    2. 2 observations
    3. 7 observations
    4. 6 observations

  3. 4.3. Using the displayed bin boundaries, what is the approximate range represented by the nonempty bins?

    1. 14
    2. 13
    3. 20
    4. 12
Histogram 5Pet WeightsWeights of pets recorded at a community event
0 up to 5: 4 observations; 5 up to 10: 9 observations; 10 up to 15: 14 observations; 15 up to 20: 10 observations; 20 up to 25: 5 observations; 25 up to 30: 0 observations; 30 up to 35: 2 observations048121605101520253035Weight (lb)Frequency

  1. 5.1. Which value is the best estimate of the distribution's center (weight (lb))?

    1. 15
    2. 16
    3. 10
    4. 20

  2. 5.2. Which description best matches the distribution's shape?

    1. Skewed left
    2. Approximately uniform
    3. Approximately symmetric
    4. Has a separated high region

  3. 5.3. Which interval may contain unusually high observations separated from the main distribution?

    1. 10–15
    2. 30–35
    3. 15–20
    4. 5–10
Histogram 6Test ScoresScores from a recent class assessment
30 up to 40: 1 observations; 40 up to 50: 3 observations; 50 up to 60: 10 observations; 60 up to 70: 14 observations; 70 up to 80: 11 observations; 80 up to 90: 4 observations; 90 up to 100: 2 observations048121630405060708090100ScoreFrequency

  1. 6.1. Which statement is directly supported by the histogram?

    1. 60–70 contains no observations.
    2. The exact median can be read from one bar.
    3. 60–70 contains the greatest number of observations.
    4. 60–70 contains the exact mean.

  2. 6.2. Which value is the best estimate of the distribution's center (score)?

    1. 85
    2. 65
    3. 75
    4. 66

  3. 6.3. Approximately what percentage of observations fall from 70 up to but not including 90?

    1. 34%
    2. 43%
    3. 48%
    4. 33%
Histogram 7Commute TimesOne-way commute times reported by adults
0 up to 10: 2 observations; 10 up to 20: 5 observations; 20 up to 30: 9 observations; 30 up to 40: 13 observations; 40 up to 50: 9 observations; 50 up to 60: 5 observations; 60 up to 70: 2 observations0481216010203040506070MinutesFrequency

  1. 7.1. What is the width of each histogram bin?

    1. 5
    2. 15
    3. 10
    4. 20

  2. 7.2. Which statement is directly supported by the histogram?

    1. 30–40 contains the greatest number of observations.
    2. The exact median can be read from one bar.
    3. 30–40 contains no observations.
    4. 30–40 contains the exact mean.

  3. 7.3. Using the displayed bin boundaries, what is the approximate range represented by the nonempty bins?

    1. 60
    2. 70
    3. 71
    4. 80
Histogram 8Rainfall — Group ADaily rainfall amounts recorded during a season
Histogram A
0 up to 2: 1 observations; 2 up to 4: 3 observations; 4 up to 6: 10 observations; 6 up to 8: 14 observations; 8 up to 10: 11 observations; 10 up to 12: 4 observations; 12 up to 14: 2 observations048121602468101214Rainfall (mm)Frequency
Histogram B
8 up to 10: 4 observations; 10 up to 12: 10 observations; 12 up to 14: 18 observations; 14 up to 16: 26 observations; 16 up to 18: 18 observations; 18 up to 20: 10 observations; 20 up to 22: 4 observations07142128810121416182022Rainfall (mm)Frequency

  1. 8.1. Which value is the best estimate of the distribution's center (rainfall (mm))?

    1. 9
    2. 6
    3. 5
    4. 7

  2. 8.2. Using the displayed bin boundaries, what is the approximate range represented by the nonempty bins?

    1. 16
    2. 13
    3. 14
    4. 15

  3. 8.3. Which histogram has the greater approximate center?

    1. Histogram B
    2. Histogram A
    3. Cannot be determined
    4. They have the same center
Histogram 9Pet WeightsWeights of pets recorded at a community event
0 up to 5: 4 observations; 5 up to 10: 9 observations; 10 up to 15: 14 observations; 15 up to 20: 10 observations; 20 up to 25: 5 observations; 25 up to 30: 0 observations; 30 up to 35: 2 observations048121605101520253035Weight (lb)Frequency

  1. 9.1. Using the displayed bin boundaries, what is the approximate range represented by the nonempty bins?

    1. 36
    2. 34
    3. 50
    4. 35

  2. 9.2. Which interval contains the fewest observations?

    1. 20–25
    2. 25–30
    3. 15–20
    4. 5–10

  3. 9.3. Which interval may contain unusually high observations separated from the main distribution?

    1. 30–35
    2. 20–25
    3. 10–15
    4. 15–20
Histogram 10Commute TimesOne-way commute times reported by adults
0 up to 10: 2 observations; 10 up to 20: 5 observations; 20 up to 30: 9 observations; 30 up to 40: 13 observations; 40 up to 50: 9 observations; 50 up to 60: 5 observations; 60 up to 70: 2 observations0481216010203040506070MinutesFrequency

  1. 10.1. Which statement is directly supported by the histogram?

    1. 30–40 contains no observations.
    2. Every observation is in 30–40.
    3. 30–40 contains the greatest number of observations.
    4. 30–40 contains the exact mean.

  2. 10.2. Approximately what percentage of observations fall from 10 up to but not including 30?

    1. 31%
    2. 26%
    3. 21%
    4. 46%

  3. 10.3. Which interval is the modal interval?

    1. 50–60
    2. 30–40
    3. 0–10
    4. 40–50
Histogram 11Package WeightsWeights of packages processed in one shift
0 up to 2: 3 observations; 2 up to 4: 8 observations; 4 up to 6: 13 observations; 6 up to 8: 10 observations; 8 up to 10: 0 observations; 10 up to 12: 4 observations; 12 up to 14: 1 observations048121602468101214Weight (kg)Frequency

  1. 11.1. Which interval is a gap with no observations?

    1. 10–12
    2. 4–6
    3. 12–14
    4. 8–10

  2. 11.2. Which interval contains the fewest observations?

    1. 4–6
    2. 10–12
    3. 8–10
    4. 6–8

  3. 11.3. How many observations are below 12?

    1. 34 observations
    2. 38 observations
    3. 50 observations
    4. 46 observations
Histogram 12Package WeightsWeights of packages processed in one shift
0 up to 2: 3 observations; 2 up to 4: 8 observations; 4 up to 6: 13 observations; 6 up to 8: 10 observations; 8 up to 10: 0 observations; 10 up to 12: 4 observations; 12 up to 14: 1 observations048121602468101214Weight (kg)Frequency

  1. 12.1. Which interval is a gap with no observations?

    1. 6–8
    2. 0–2
    3. 8–10
    4. 10–12

  2. 12.2. How many intervals are displayed?

    1. 7
    2. 8
    3. 9
    4. 10

  3. 12.3. Which value is the best estimate of the distribution's center (weight (kg))?

    1. 10
    2. 2
    3. 7
    4. 6
Histogram 13Commute TimesOne-way commute times reported by adults
0 up to 10: 7 observations; 10 up to 20: 6 observations; 20 up to 30: 7 observations; 30 up to 40: 6 observations; 40 up to 50: 7 observations; 50 up to 60: 6 observations; 60 up to 70: 7 observations02468010203040506070MinutesFrequency

  1. 13.1. What is the width of each histogram bin?

    1. 5
    2. 10
    3. 15
    4. 25

  2. 13.2. Which value is the best estimate of the distribution's center (minutes)?

    1. 34
    2. 15
    3. 35
    4. 45

  3. 13.3. How many observations are below 50?

    1. 33 observations
    2. 32 observations
    3. 40 observations
    4. 26 observations
Histogram 14Package WeightsWeights of packages processed in one shift
0 up to 2: 4 observations; 2 up to 4: 9 observations; 4 up to 6: 14 observations; 6 up to 8: 10 observations; 8 up to 10: 5 observations; 10 up to 12: 0 observations; 12 up to 14: 2 observations048121602468101214Weight (kg)Frequency

  1. 14.1. Which statement is directly supported by the histogram?

    1. 4–6 contains no observations.
    2. The exact median can be read from one bar.
    3. 4–6 contains the exact mean.
    4. 4–6 contains the greatest number of observations.

  2. 14.2. How many observations are below 10?

    1. 32 observations
    2. 52 observations
    3. 42 observations
    4. 37 observations

  3. 14.3. Which interval may contain unusually high observations separated from the main distribution?

    1. 12–14
    2. 0–2
    3. 6–8
    4. 8–10
Histogram 15Books ReadBooks read during a school reading challenge
0 up to 2: 6 observations; 2 up to 4: 16 observations; 4 up to 6: 26 observations; 6 up to 8: 20 observations; 8 up to 10: 0 observations; 10 up to 12: 8 observations; 12 up to 14: 2 observations0714212802468101214BooksFrequency

  1. 15.1. Which interval is the modal interval?

    1. 0–2
    2. 12–14
    3. 10–12
    4. 4–6

  2. 15.2. Approximately what percentage of observations fall from 8 up to but not including 12?

    1. 9%
    2. 10%
    3. 15%
    4. 20%

  3. 15.3. Which interval contains the value 5?

    1. 6–8
    2. 0–2
    3. 8–10
    4. 4–6
45 verified questions.mathbatch.com