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Histograms practice questions with answers

Higher · Grade 7 · Calculator

A second set of histograms questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

A histogram bar has frequency density 3 and class width 10. Calculate the frequency.

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Answer: 30

  1. Area = density × width.
  2. 3 × 10 = 30.
  • Method (1): Area = density × width.
  • Accuracy (1): 3 × 10 = 30.

Question 2 Easy

A class interval has frequency 24 and class width 8. Calculate the frequency density.

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Answer: 3

  1. Density = frequency ÷ width.
  2. 24 ÷ 8 = 3.
  • Method (1): Density = frequency ÷ width.
  • Accuracy (1): 24 ÷ 8 = 3.

Question 3 Medium

Calculate the total frequency of two bars, density 3 width 4 and density 2 width 5.

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Answer: 22

  1. First bar: 3 × 4 = 12. Second bar: 2 × 5 = 10.
  2. Total: 12 + 10 = 22.
  • Method (1): First bar: 3 × 4 = 12. Second bar: 2 × 5 = 10.
  • Accuracy (1): Total: 12 + 10 = 22.

Question 4 Medium

Calculate the total frequency of two bars, density 5 width 2 and density 1 width 10.

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Answer: 20

  1. First bar: 5 × 2 = 10. Second bar: 1 × 10 = 10.
  2. Total: 10 + 10 = 20.
  • Method (1): First bar: 5 × 2 = 10. Second bar: 1 × 10 = 10.
  • Accuracy (1): Total: 10 + 10 = 20.

Question 5 Hard

Which frequency is larger: density 4 width 5, or density 2 width 10?

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Answer: equal

  1. First bar: 4 × 5 = 20. Second bar: 2 × 10 = 20.
  2. Both areas are 20, so they are equal.
  • Method (1): First bar: 4 × 5 = 20. Second bar: 2 × 10 = 20.
  • Accuracy (1): Both areas are 20, so they are equal.

Question 6 Hard

A class interval has frequency 36 and class width 9. Calculate the frequency density.

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Answer: 4

  1. Density = frequency ÷ width.
  2. 36 ÷ 9 = 4.
  • Method (1): Density = frequency ÷ width.
  • Accuracy (1): 36 ÷ 9 = 4.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A histogram bar has frequency density 8 and class width 5. Calculate the frequency.

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Answer: 40

  1. State formula: Frequency = Frequency Density × Class Width.
  2. Multiply values: 8 × 5 = 40.
  • Method (1): 8 × 5
  • Accuracy (1): 40

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What does the area of each bar in a histogram represent?

  1. the frequency of the class interval
  2. the class width
  3. the cumulative frequency
  4. the mean value
Show answer

the frequency of the class interval In a histogram, Area = Frequency Density × Class Width = Frequency.

Check 2

A bar has frequency density 4 and class width 5. What is the frequency?

  1. 20
  2. 9
  3. 4
  4. 0.8
Show answer

20 Frequency = 4 × 5 = 20.

Check 3

Why is adding frequency density and class width incorrect?

  1. frequency is the area (product), not the sum
  2. the units are the same
  3. frequency is always smaller than density
  4. addition is only for bar charts
Show answer

frequency is the area (product), not the sum The area of a rectangular bar is width multiplied by height.

Check 4

A class interval has frequency 30 and class width 10. What is the frequency density?

  1. 3
  2. 300
  3. 20
  4. 0.33
Show answer

3 Frequency density = 30 ÷ 10 = 3.

Check 5

How do you find the frequency of a bar when class widths are unequal?

  1. multiply each bar’s density by its own width
  2. multiply density by 10 for all bars
  3. divide density by the average width
  4. read the height directly
Show answer

multiply each bar’s density by its own width Each bar’s frequency is its unique density multiplied by its specific width.

Check 6

Two histogram bars have areas 10 and 40. What is the total frequency?

  1. 50
  2. 30
  3. 400
  4. 4
Show answer

50 Total frequency = 10 + 40 = 50.

Check 7

Which bar has greater frequency: density 6 width 4, or density 3 width 5?

  1. the first bar (area 24 vs 15)
  2. the second bar
  3. both are equal
  4. cannot be determined
Show answer

the first bar (area 24 vs 15) First bar area = 6 × 4 = 24. Second bar area = 3 × 5 = 15.

Check 8

Which bar has greater frequency: density 2 width 6, or density 5 width 4?

  1. the second bar (area 20 vs 12)
  2. the first bar
  3. both are equal
  4. cannot be determined
Show answer

the second bar (area 20 vs 12) First bar area = 2 × 6 = 12. Second bar area = 5 × 4 = 20.

Check 9

When do two histogram bars with different heights represent equal frequencies?

  1. when their products of density and width are equal
  2. when their widths are equal
  3. never, taller bars always have more
  4. when both densities are prime
Show answer

when their products of density and width are equal Equal areas mean equal frequencies: d₁ × w₁ = d₂ × w₂.

Check 10

What is plotted on the vertical axis of a histogram?

  1. frequency density
  2. frequency
  3. cumulative frequency
  4. class width
Show answer

frequency density The vertical axis shows frequency density.

Check 11

A bar has frequency 40 and class width 5. What is the frequency density?

  1. 8
  2. 200
  3. 35
  4. 45
Show answer

8 Frequency density = 40 ÷ 5 = 8.

Check 12

A bar has frequency density 3 and class width 10. What is the frequency?

  1. 30
  2. 13
  3. 3.33
  4. 0.3
Show answer

30 Frequency = 3 × 10 = 30.

Check 13

Why can a tall narrow bar have a lower frequency than a short wide bar?

  1. area depends on width as well as height
  2. narrow bars are drawn incorrectly
  3. height always determines frequency
  4. histograms only use equal widths
Show answer

area depends on width as well as height A short wide bar can have a larger area than a tall narrow bar.

Check 14

A class interval has frequency 18 and class width 6. What is the frequency density?

  1. 3
  2. 108
  3. 12
  4. 24
Show answer

3 Frequency density = 18 ÷ 6 = 3.

Check 15

How do you find the total frequency across an entire histogram?

  1. sum the areas of all the bars
  2. add all the frequency densities
  3. multiply total width by highest density
  4. count the number of bars
Show answer

sum the areas of all the bars Total frequency is the sum of all individual bar areas.

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