Histograms
A histogram is a chart for continuous grouped data in which the bars touch, because the data runs continuously along the horizontal axis with no gaps between classes. For equal-width class intervals, the height of each bar shows the frequency for that class. Histograms appear in GCSE Statistics when summarising numerical data such as heights, times or masses.
Before you start
Make sure you're comfortable with these topics first:
Method
- Check that the data is continuous and grouped into class intervals with no gaps between them, for example 10-20, 20-30.
- Draw the horizontal axis to represent the continuous variable and the vertical axis to represent frequency, when all class widths are equal.
- For each class, draw a bar whose width matches the class interval and whose height equals the frequency for that class.
- Make sure every bar touches the bars either side of it, since there is no gap between continuous classes.
- Label both axes clearly with units, and give the histogram a title describing what it shows.
- Read values off the histogram by matching a bar's height to the frequency axis, or add several bar heights together to find a total frequency.
Worked example
A histogram for the masses, in kg, of 60 parcels has five bars of equal width 5 kg, covering the class intervals 0-5, 5-10, 10-15, 15-20 and 20-25. The bar heights (frequencies) are 6, 18, 20, 10 and an unknown value for the last class. Find the height of the missing bar.
- Since all the class widths are equal (5 kg), the height of each bar is simply the frequency for that class.
- Add the four known frequencies: 6 + 18 + 20 + 10 = 54.
- The total frequency for all 60 parcels must be 60, so the missing frequency is 60 - 54 = 6.
- The missing bar therefore has a height of 6.
- Final answer: the missing bar has height 6 (frequency 6).
Practice questions
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Q1A histogram has bars of equal width. True or false: the height of each bar represents the frequency for that class.Show answer
Answer: True (for equal class widths, height = frequency).
Q2State one reason why a histogram has no gaps between its bars, unlike a bar chart.Show answer
Answer: Because it displays continuous data, which flows without gaps between class intervals.
Q3A histogram for exam scores has bars of equal width 10 marks, covering 0-10, 10-20, 20-30, 30-40, with heights 2, 8, 15, 5. How many students took the exam?Show answer
Answer: 30 students (2 + 8 + 15 + 5 = 30).
Q4Using the same histogram, how many students scored between 10 and 30 marks?Show answer
Answer: 23 students (8 + 15 = 23).
Q5A histogram of ages has 5 equal-width bars covering 0-10, 10-20, 20-30, 30-40, 40-50 with heights 3, 7, x, 9, 2, and a total of 35 people. Find x.Show answer
Answer: x = 14 (35 - (3+7+9+2) = 14).
Q6A histogram has unequal class widths. Explain why the height of a bar can no longer be read directly as the frequency.Show answer
Answer: With unequal widths, frequency is shown by the bar's area, not its height, so height (frequency density) must be multiplied by class width to get frequency.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
The table shows the heights, in cm, of 50 seedlings. Height (cm): 0-10 freq 5; 10-20 freq 17; 20-30 freq 20; 30-40 freq 8. All class widths are equal. A histogram is drawn for this data. State the height of the bar representing the class 20-30 cm, and calculate how many seedlings are shorter than 20 cm.
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60 employees' commuting times, in minutes, are grouped into 4 equal-width classes of width 15 minutes: 0-15, 15-30, 30-45, 45-60. The frequencies for the first three classes are 8, 22 and 19. A histogram is drawn using these frequencies as bar heights. Find the frequency of the final class, and state the height of the bar for the class 15-30 minutes.
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Explain why it would be incorrect to draw a histogram for the data 'favourite colour' collected from a class of students.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the histograms worksheet pack - 15 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 19 of GCSE Statistics Foundation Workbook 1 and chapter 23 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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