Bar charts and honest scales
Represent categorical or discrete frequencies using separated bars and readable axes.
Core and Extended. This is the separate 9–1 qualification 0980. Cambridge intends Core for grades 4–1 and Extended for grades 9–5; the eligible award bands are grades 5–1 for the Core papers and grades 9–3 for the Extended papers.
Before you begin
- Read frequency tables.
- Choose a uniform numerical scale.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What represents frequency in an ordinary bar chart?
What you will learn
- Construct and interpret a bar chart.
- Recognise misleading or inconsistent scales.
Bar height represents frequency
A bar chart for bus 18, car 10, walk 8 and cycle 4 uses four labelled categories. Give bars equal widths and gaps, and use a consistent vertical scale labelled frequency. The height of the bus bar is eighteen; its area is not the quantity being compared.
Separated bars suit categories or discrete values. A histogram instead represents continuous class intervals, with touching bars and frequency related to area. Do not call every rectangular frequency graphic a histogram: the axis meanings and grouping determine its type.
A clear scale supports fair comparison
A zero baseline lets bar heights show proportional frequencies. If the axis begins at eight, frequencies ten and twelve can look far more different than their counts justify. Read actual values and label a deliberate axis break if one is used; use a zero baseline for ordinary school bar-chart construction.
Choose evenly spaced tick intervals that cover the largest value, label both axes and include context. Decorative three-dimensional bars can obscure heights, so use simple rectangles. Check that the plotted frequencies sum to the table total when the categories are exhaustive.
Pause and explain
Bus 18, car 10, walk 8, cycle 4. What is the total frequency?
Worked example
Construct a bar chart for bus 18, car 10, walk 8, cycle 4.
Show the worked solution
- Label the horizontal axis travel method and vertical axis frequency.
- Use a zero baseline with evenly spaced ticks reaching at least eighteen.
- Draw equal-width separated bars with heights 18,10,8,4; total frequency forty.
Answer Four separated bars at 18,10,8,4 on a labelled frequency scale.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Draw bars for frequencies A = 3, B = 7, C = 5.
Give me a hint
Choose a zero baseline and a uniform scale.
Compare my reasoning
- Label categories A,B,C with separated equal-width bars.
- Use frequency ticks from zero through at least seven.
- Bar heights are three, seven and five; total fifteen.
Separated bars of heights 3,7,5.
Look for these in your work
- Used clear axes.
- Matched the table counts.
A chart has category counts 12,18,10. Find the percentage in the second category.
Give me a hint
Use the grand total as the denominator.
Compare my reasoning
- Total is forty.
- Second-category fraction is 18/40.
- Percentage is forty-five percent.
45%.
Look for these in your work
- Read the correct bar.
- Used the full total.
Why can bars for 10 and 12 look misleading when a vertical scale begins at 9?
Give me a hint
Compare visible lengths with actual values.
Compare my reasoning
- Visible lengths become one and three rather than ten and twelve.
- That suggests a threefold difference although the counts differ by twenty percent.
- Use a zero baseline or clearly disclose the truncated scale when interpreting.
The truncated baseline exaggerates the visual difference.
Look for these in your work
- Used actual values.
- Explained the scale effect.
Common mistakes
- Uneven numerical tick spacing.
- Unlabelled axes.
- Confusing bar height with histogram area.
What can you explain now?
Should categorical bars normally touch?
Compare with the explanation
No.
Gaps distinguish categories, unlike a continuous-interval histogram.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, construct a bar chart from a table and check its total and scale.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.