IGCSE Mathematics: Statistical Diagrams Practice Questions
A pie chart divides 360 degrees in proportion to the frequencies, so each item's angle is its frequency divided by the total, multiplied by 360. A scatter diagram shows the relationship between two variables.
Topic 9.3 of Cambridge IGCSE Mathematics 0580 tests reading diagrams as much as drawing them. Pie chart questions run in both directions, from frequency to angle and back again. The questions below cover both, plus correlation.
What you need to know for Statistical Diagrams
- Pie chart angleAngle = (frequency divided by total frequency) x 360 degrees. All the angles must add to 360.
- Reading a pie chart backwardsFrequency = (angle divided by 360) x total. You need the overall total to convert an angle into a number.
- Bar chartBars of equal width with gaps between them, used for discrete or categorical data. The height shows the frequency.
- Scatter diagramPlots pairs of values to show whether two variables are related. Each point represents one item with two measurements.
- CorrelationPositive means one rises as the other rises. Negative means one falls as the other rises. Strength is described as strong or weak depending on how close the points lie to a line.
- Line of best fitA single straight line drawn through the trend of the points, with roughly as many above as below. Use it to estimate values, but only within the range of the data.
IGCSE Mathematics Statistical Diagrams questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
In a survey of 45 students, 12 chose football as their favourite sport. Calculate the angle of the football sector in a pie chart, correct to the nearest degree.
Show the worked answer
- A pie chart represents the whole data set with 360 degrees.
- The fraction choosing football is 12 out of 45.
- Angle = (12 divided by 45) x 360.
- 12 divided by 45 = 0.26667, and 0.26667 x 360 = 96 degrees.
A pie chart represents 60 people. One sector has an angle of 72 degrees. Calculate how many people that sector represents.
Show the worked answer
- The whole pie chart of 360 degrees represents all 60 people.
- The fraction of the chart taken by the sector is 72 divided by 360 = one fifth.
- Frequency = one fifth x 60.
- The sector represents 12 people.
A scatter diagram plots hours of revision against exam score for a class. The points slope upwards from left to right and lie fairly close to a straight line. Describe the correlation and explain what it suggests.
Show the worked answer
- The points slope upwards from left to right, so as revision hours increase, exam scores increase. That is positive correlation.
- The points lie fairly close to a straight line, so the correlation is strong rather than weak.
- This suggests that students who revised for longer tended to achieve higher scores.
- Correlation does not prove that revision caused the higher scores. Another factor, such as general motivation, could influence both.
Explain how to draw a line of best fit on a scatter diagram, and state one limitation of using it to make predictions.
Show the worked answer
- Draw one straight line that follows the overall trend of the plotted points.
- Position it so that roughly as many points lie above the line as below it, and so that the points are as close to it as possible.
- It does not have to pass through the origin or through any particular plotted point.
- The main limitation is that predictions outside the range of the collected data are unreliable, because there is no evidence the trend continues beyond the values measured.
Common mistakes in this topic
- Using 100 instead of 360 for pie chart angles.
- Failing to check that pie chart angles total 360 degrees.
- Claiming correlation proves causation.
- Joining scatter points instead of drawing a single straight line.
- Predicting far outside the range of the data.
Exam tips
- Check that all your pie chart angles add to 360 before drawing.
- Describe correlation with two words: strength and direction, for example strong negative.
- Always interpret correlation in the context of the two variables, not in general terms.
- Draw a line of best fit with a ruler and a sharp pencil, and use it to read values by drawing dashed lines across.
- Mention the limitation about extrapolating beyond the data if the question asks about reliability.
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Statistical Diagrams FAQs
How do I calculate a pie chart angle?
Divide the frequency by the total frequency, then multiply by 360. So 12 out of 45 students gives an angle of 12 divided by 45, multiplied by 360, which is 96 degrees. Check that all your angles add to 360.
How do I read a frequency from a pie chart?
Divide the sector angle by 360 to find the fraction of the whole it represents, then multiply that fraction by the total frequency. A 72 degree sector of a chart representing 60 people accounts for one fifth of them, which is 12.
How do I describe correlation?
Give both the direction and the strength. Direction is positive if one variable rises as the other rises, and negative if one falls as the other rises. Strength depends on how closely the points cluster around a straight line, described as strong or weak.
Does correlation mean one thing causes the other?
No. Correlation shows only that two variables are associated. A third factor could be influencing both, or the relationship could be coincidental. Stating causation from a scatter diagram alone is a common way to lose a mark.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.