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

    1. 0–2
    2. 8–10
    3. 4–6
    4. 12–14

  2. How many observations fall from 4 up to but not including 8?

    1. 24 observations
    2. 44 observations
    3. 54 observations
    4. 23 observations

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

    1. 12
    2. 10
    3. 6
    4. 5
Histogram 2Package 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. Which interval is a gap with no observations?

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

  2. How many intervals are displayed?

    1. 8
    2. 7
    3. 6
    4. 5

  3. Which statement is directly supported by the histogram?

    1. 4–6 contains the exact mean.
    2. The exact median can be read from one bar.
    3. 4–6 contains the greatest number of observations.
    4. Every observation is in 4–6.
Histogram 3Exercise MinutesDaily exercise time recorded by students
0 up to 15: 4 observations; 15 up to 30: 9 observations; 30 up to 45: 14 observations; 45 up to 60: 10 observations; 60 up to 75: 5 observations; 75 up to 90: 0 observations; 90 up to 105: 2 observations04812160153045607590105MinutesFrequency

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

    1. 45
    2. 30
    3. 75
    4. 90

  2. Which interval is a gap with no observations?

    1. 30–45
    2. 90–105
    3. 15–30
    4. 75–90

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

    1. 60–75
    2. 90–105
    3. 75–90
    4. 30–45
Histogram 4Plant HeightsHeights of plants in a classroom experiment
10 up to 15: 4 observations; 15 up to 20: 9 observations; 20 up to 25: 14 observations; 25 up to 30: 10 observations; 30 up to 35: 5 observations; 35 up to 40: 0 observations; 40 up to 45: 2 observations04812161015202530354045Height (cm)Frequency

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

    1. 10–15
    2. 30–35
    3. 40–45
    4. 35–40

  2. Approximately what percentage of observations fall from 30 up to but not including 40?

    1. 21%
    2. 10%
    3. 26%
    4. 11%

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

    1. 25
    2. 26
    3. 24
    4. 30
Histogram 5Exercise MinutesDaily exercise time recorded by students
0 up to 15: 1 observations; 15 up to 30: 3 observations; 30 up to 45: 10 observations; 45 up to 60: 14 observations; 60 up to 75: 11 observations; 75 up to 90: 4 observations; 90 up to 105: 2 observations04812160153045607590105MinutesFrequency

  1. Which interval is the modal interval?

    1. 45–60
    2. 90–105
    3. 60–75
    4. 15–30

  2. How many observations are below 30?

    1. 5 observations
    2. 1 observations
    3. 3 observations
    4. 4 observations

  3. Which interval is at the center of the largest visible cluster?

    1. 30–45
    2. 45–60
    3. 60–75
    4. 75–90
Histogram 6Commute Times — Group AOne-way commute times reported by adults
Histogram A
0 up to 10: 3 observations; 10 up to 20: 8 observations; 20 up to 30: 13 observations; 30 up to 40: 10 observations; 40 up to 50: 0 observations; 50 up to 60: 4 observations; 60 up to 70: 1 observations0481216010203040506070MinutesFrequency
Histogram B
20 up to 30: 14 observations; 30 up to 40: 11 observations; 40 up to 50: 8 observations; 50 up to 60: 5 observations; 60 up to 70: 3 observations; 70 up to 80: 2 observations; 80 up to 90: 1 observations04812162030405060708090MinutesFrequency

  1. Which histogram has the greater approximate center?

    1. Histogram A
    2. Cannot be determined
    3. Histogram B
    4. They have the same center

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

    1. 40
    2. 30
    3. 31
    4. 10

  3. Which interval is a gap with no observations?

    1. 10–20
    2. 60–70
    3. 30–40
    4. 40–50
Histogram 7Rainfall — Group ADaily rainfall amounts recorded during a season
Histogram A
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 observations048121602468101214Rainfall (mm)Frequency
Histogram B
4 up to 6: 4 observations; 6 up to 8: 10 observations; 8 up to 10: 18 observations; 10 up to 12: 26 observations; 12 up to 14: 18 observations; 14 up to 16: 10 observations; 16 up to 18: 4 observations071421284681012141618Rainfall (mm)Frequency

  1. Which histogram has the greater approximate center?

    1. Histogram A
    2. They have the same center
    3. Histogram B
    4. Cannot be determined

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

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

  3. How many observations fall from 8 up to but not including 10?

    1. 0 observations
    2. 5 observations
    3. 10 observations
    4. 20 observations
Histogram 8Practice Shots — Group APoints scored during basketball practice rounds
Histogram A
0 up to 5: 2 observations; 5 up to 10: 5 observations; 10 up to 15: 9 observations; 15 up to 20: 13 observations; 20 up to 25: 9 observations; 25 up to 30: 5 observations; 30 up to 35: 2 observations048121605101520253035PointsFrequency
Histogram B
10 up to 15: 1 observations; 15 up to 20: 2 observations; 20 up to 25: 3 observations; 25 up to 30: 5 observations; 30 up to 35: 8 observations; 35 up to 40: 11 observations; 40 up to 45: 14 observations04812161015202530354045PointsFrequency

  1. Approximately what percentage of observations fall from 25 up to but not including 35?

    1. 15%
    2. 11%
    3. 31%
    4. 16%

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

    1. 18.5
    2. 22.5
    3. 17.5
    4. 16.5

  3. Which histogram has the greater approximate center?

    1. Histogram B
    2. They have the same center
    3. Cannot be determined
    4. Histogram A
Histogram 9Plant HeightsHeights of plants in a classroom experiment
10 up to 15: 8 observations; 15 up to 20: 18 observations; 20 up to 25: 28 observations; 25 up to 30: 20 observations; 30 up to 35: 10 observations; 35 up to 40: 0 observations; 40 up to 45: 4 observations071421281015202530354045Height (cm)Frequency

  1. Which interval is a gap with no observations?

    1. 20–25
    2. 25–30
    3. 30–35
    4. 35–40

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

    1. 25
    2. 35
    3. 36
    4. 34

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

    1. 40–45
    2. 25–30
    3. 35–40
    4. 30–35
Histogram 10Rainfall — Group ADaily rainfall amounts recorded during a season
Histogram A
0 up to 2: 2 observations; 2 up to 4: 5 observations; 4 up to 6: 9 observations; 6 up to 8: 13 observations; 8 up to 10: 9 observations; 10 up to 12: 5 observations; 12 up to 14: 2 observations048121602468101214Rainfall (mm)Frequency
Histogram B
4 up to 6: 1 observations; 6 up to 8: 2 observations; 8 up to 10: 3 observations; 10 up to 12: 5 observations; 12 up to 14: 8 observations; 14 up to 16: 11 observations; 16 up to 18: 14 observations04812164681012141618Rainfall (mm)Frequency

  1. How many observations fall from 10 up to but not including 12?

    1. 15 observations
    2. 6 observations
    3. 5 observations
    4. 4 observations

  2. Which histogram has the greater approximate center?

    1. Histogram B
    2. Histogram A
    3. Cannot be determined
    4. They have the same center

  3. Which description best matches the distribution's shape?

    1. Skewed left
    2. Approximately symmetric
    3. Skewed right
    4. Approximately uniform
Histogram 11Reaction TimesReaction times from a classroom activity
150 up to 200: 6 observations; 200 up to 250: 16 observations; 250 up to 300: 26 observations; 300 up to 350: 20 observations; 350 up to 400: 0 observations; 400 up to 450: 8 observations; 450 up to 500: 2 observations07142128150200250300350400450500MillisecondsFrequency

  1. Which interval is the modal interval?

    1. 350–400
    2. 150–200
    3. 200–250
    4. 250–300

  2. How many observations are below 450?

    1. 100 observations
    2. 77 observations
    3. 76 observations
    4. 68 observations

  3. Which statement is directly supported by the histogram?

    1. The exact median can be read from one bar.
    2. 250–300 contains the greatest number of observations.
    3. Every observation is in 250–300.
    4. 250–300 contains no observations.
Histogram 12RainfallDaily rainfall amounts recorded during a season
0 up to 2: 14 observations; 2 up to 4: 11 observations; 4 up to 6: 8 observations; 6 up to 8: 5 observations; 8 up to 10: 3 observations; 10 up to 12: 2 observations; 12 up to 14: 1 observations048121602468101214Rainfall (mm)Frequency

  1. Which description best matches the distribution's shape?

    1. Approximately symmetric
    2. Skewed left
    3. Skewed right
    4. Approximately uniform

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

    1. 11%
    2. 10%
    3. 6%
    4. 1%

  3. Which interval contains the value 9?

    1. 2–4
    2. 10–12
    3. 0–2
    4. 8–10
Histogram 13Package WeightsWeights of packages processed in one shift
0 up to 2: 2 observations; 2 up to 4: 6 observations; 4 up to 6: 20 observations; 6 up to 8: 28 observations; 8 up to 10: 22 observations; 10 up to 12: 8 observations; 12 up to 14: 4 observations0714212802468101214Weight (kg)Frequency

  1. Which statement is directly supported by the histogram?

    1. The exact median can be read from one bar.
    2. 6–8 contains the greatest number of observations.
    3. 6–8 contains no observations.
    4. 6–8 contains the exact mean.

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

    1. 15
    2. 13
    3. 14
    4. 18

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

    1. 33%
    2. 32%
    3. 38%
    4. 28%
Histogram 14Practice Shots — Group APoints scored during basketball practice rounds
Histogram A
0 up to 5: 1 observations; 5 up to 10: 3 observations; 10 up to 15: 10 observations; 15 up to 20: 14 observations; 20 up to 25: 11 observations; 25 up to 30: 4 observations; 30 up to 35: 2 observations048121605101520253035PointsFrequency
Histogram B
10 up to 15: 4 observations; 15 up to 20: 10 observations; 20 up to 25: 18 observations; 25 up to 30: 26 observations; 30 up to 35: 18 observations; 35 up to 40: 10 observations; 40 up to 45: 4 observations071421281015202530354045PointsFrequency

  1. Which interval is the modal interval?

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

  2. Which histogram has the greater approximate center?

    1. Histogram A
    2. Cannot be determined
    3. Histogram B
    4. They have the same center

  3. Which statement is directly supported by the histogram?

    1. 15–20 contains the greatest number of observations.
    2. 15–20 contains no observations.
    3. The exact median can be read from one bar.
    4. 15–20 contains the exact mean.
Histogram 15Commute Times — Group AOne-way commute times reported by adults
Histogram A
0 up to 10: 2 observations; 10 up to 20: 4 observations; 20 up to 30: 6 observations; 30 up to 40: 10 observations; 40 up to 50: 16 observations; 50 up to 60: 22 observations; 60 up to 70: 28 observations07142128010203040506070MinutesFrequency
Histogram B
20 up to 30: 14 observations; 30 up to 40: 11 observations; 40 up to 50: 8 observations; 50 up to 60: 5 observations; 60 up to 70: 3 observations; 70 up to 80: 2 observations; 80 up to 90: 1 observations04812162030405060708090MinutesFrequency

  1. Which histogram has the greater approximate center?

    1. Cannot be determined
    2. They have the same center
    3. Histogram B
    4. Histogram A

  2. Which interval contains the fewest observations?

    1. 10–20
    2. 0–10
    3. 60–70
    4. 40–50

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

    1. 1%
    2. 21%
    3. 16%
    4. 11%
45 verified questions.mathbatch.com
Learn the skill

What is 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.

How to solve histograms

  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.

Worked example

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

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.