Choose the display that matches the type of data and the question you want answered. Categories suit bar charts and pie charts, grouped measurements suit histograms and cumulative frequency curves, and two measured variables suit a scatter diagram.
This skill belongs to data displays and cumulative reasoning. It ties together histograms, cumulative frequency and scatter diagrams, and it helps you explain a choice in words.
Which display fits which question?
| Question you want to answer | Suitable display | Why |
|---|---|---|
| How many fall in each category? | Bar chart | Separate bars, heights compare counts |
| What share of one whole is each category? | Pie chart | Angles show fractions of the total |
| How is a continuous measurement spread across unequal classes? | Histogram | Area shows frequency, so width differences are handled |
| What are the median and quartiles of grouped data? | Cumulative frequency curve | Read at n/2, n/4, 3n/4 |
| Are two measured variables related? | Scatter diagram | Each point holds two values |
| How does one quantity change over time? | Line graph | Order along the horizontal axis has meaning |
How to decide, step by step
- Name the data type: categories, discrete numbers, or continuous measurements.
- Name the question: counts, shares, spread, median, relationship or change.
- Match them using the table above.
- Check the scale and labels so the picture cannot mislead.
- Justify in one sentence why the display suits the data.
Worked example
A student has RM240 pocket money for a month. The amounts are: food RM120, transport RM60, savings RM40, other RM20.
(a) Which display shows the share of each item? The question is about shares of one whole, so a pie chart suits it.
(b) Find the angle for each sector. Each angle is amount ÷ 240 × 360°.
Step 1: food 120 ÷ 240 × 360 = 180°.
Step 2: transport 60 ÷ 240 × 360 = 90°.
Step 3: savings 40 ÷ 240 × 360 = 60°.
Step 4: other 20 ÷ 240 × 360 = 30°.
Step 5, check: 180 + 90 + 60 + 30 = 360°.
(c) Is a pie chart a good way to compare this student’s budget with a friend’s budget of RM480? Not on its own. The two pies would have the same size, so the totals are hidden. A bar chart using amounts in RM would show the real difference.
The mistake to watch for
The usual slip is letting equal angles stand in for equal numbers.
Mistaken answer: “Both pie charts have a 90° sector for walking, so the same number of students walk in both surveys.”
The student forgot that the surveys have different totals. In Survey A, 10 of 40 students walk. In Survey B, 30 of 120 students walk. Both are 90°, but 10 ≠ 30.
The correction is to read the total beside each pie chart and state that angles show proportions, not counts. A second common misuse is to draw a histogram with heights equal to frequency when the classes have unequal widths, which overstates the wider classes.
Check yourself
Try these, then open each answer.
1. Which display would you choose to show the relationship between hours of sleep and exam score for 30 students?
Show answer
A scatter diagram, because each student gives two measured values and you want to see if they are associated.
2. In a survey of 60 students, 14 cycle to school. What is the angle of the “cycle” sector in a pie chart?
Show answer
14 ÷ 60 × 360 = 14 × 6 = 84°.
3. You have the lengths of 120 phone calls grouped into classes and want the median. Which display do you use and what position do you read?
Show answer
Draw a cumulative frequency curve. Read across at the 120 ÷ 2 = 60th value, then down to the time axis.
Where this leads next
Put the whole module together with the data displays practice set. You can also revisit comparing two distributions to see how a choice of display affects fairness. The percentage-base explorer helps when converting counts to shares, and the non-calculator working trainer supports the arithmetic.
Some students know each chart but still pick the wrong one under pressure. In online one-to-one Mathematics tuition, a teacher can ask why you chose each display and tighten your routine.