Pie charts and pictogram keys
Turn category proportions into angles and interpret symbols using their stated key.
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
- Use fractions of 360 degrees.
- Multiply proportions by totals.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What total angle represents a complete pie chart?
What you will learn
- Calculate pie-sector angles from frequencies.
- Read complete and partial pictogram symbols.
Every pie sector is a fraction of the whole
A pie chart's full turn is 360°. A category's sector angle is its frequency divided by total frequency, multiplied by 360. In forty journeys, eighteen bus journeys give 18/40 × 360 = 162°. Frequencies 10,8,4 give angles 90°,72°,36° respectively.
Use a protractor to mark angles around one centre, with labels or a legend. Angles should sum to 360°. A pie chart shows proportions; comparing two pies alone may not reveal which population is larger unless their totals are stated.
A pictogram symbol has a numerical meaning
If a full book symbol represents four books, three full symbols and one half-symbol represent 3×4 + 2 = 14 books. The key must state the value of one symbol. A half-symbol means half the key value, not automatically one observation.
Use consistently sized symbols and clearly defined fractions of a symbol. Enlarging a symbol in both width and height can accidentally imply area scaling, so count repeated standard symbols. To recover a frequency from a pie chart, multiply its angle fraction by the total number.
Pause and explain
A full pictogram symbol means four books. What do three full and one half-symbol mean?
Worked example
A group has forty journeys and eighteen are by bus. Find the bus pie-sector angle.
Show the worked solution
- Bus proportion is 18/40.
- Multiply by the full turn: (18/40)×360.
- The angle is 162°, and remaining categories must fill 198°.
Answer 162°.
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.
Ten of forty journeys are by car. Find its pie angle.
Give me a hint
One quarter of the group takes one quarter of the circle.
Compare my reasoning
- Fraction is 10/40 = 1/4.
- Angle is 360/4.
- The sector is 90°.
90°.
Look for these in your work
- Used the total frequency.
- Converted a proportion to an angle.
A 72° sector represents a category in a group of fifty. Find its frequency.
Give me a hint
Reverse the angle calculation.
Compare my reasoning
- The sector fraction is 72/360 = 1/5.
- Multiply by fifty.
- The category contains ten observations.
10.
Look for these in your work
- Used the full-turn denominator.
- Recovered the count from the proportion.
A pictogram key gives six learners per symbol. A row shows two full and a third of a symbol. Find the count.
Give me a hint
Apply the key to the partial symbol too.
Compare my reasoning
- Two full symbols represent twelve.
- One third of six represents two.
- Total count is fourteen learners.
14 learners.
Look for these in your work
- Applied the key consistently.
- Interpreted the symbol fraction.
Common mistakes
- Using a percentage directly as an angle.
- Ignoring pictogram keys.
- Comparing pie counts without population totals.
What can you explain now?
Can equal pie proportions prove equal category counts in two groups?
Compare with the explanation
No.
Counts also depend on the groups' total sizes, which a proportion alone does not show.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, convert one frequency to a sector angle and back, then read a partial pictogram symbol.
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.