Presenting Data: Bar Charts, Pie Charts and Two-Way Tables
Learn how to present data clearly using the four key methods tested in IGCSE Maths: two-way tables, pictograms, bar charts, and pie charts. This topic covers how to read and complete a two-way table, how to draw accurate bar charts, and how to calculate sector angles for pie charts using the formula (frequency ÷ total) × 360°. Worked examples and an auto-marked practice room are included to build confidence before your exam.
Once data has been collected, it needs to be presented clearly so it is easy to read and interpret. The four main methods covered at IGCSE are two-way tables, pictograms, bar charts, and pie charts. Knowing when to use each one is just as important as knowing how to draw it.
Two-Way Tables
Organises data by two categories at once. Row and column totals make comparisons straightforward.
Pictograms
Uses a repeated symbol to represent values, with a key showing the value of each symbol.
Bar Charts
Bars of equal width show the frequency of each category. Best for categorical and discrete data.
Pie Charts
A circle divided into sectors proportional to frequency. Good for comparing parts of a whole.
Two-Way Tables
A two-way table organises data using two grouping variables: one along the rows and one along the columns. Each cell shows the count for that specific combination. A totals column and totals row are always required.
How to read and use a two-way table
- Identify the two variables (the row heading and the column heading).
- Read individual cells to find the count for a specific combination of categories.
- Use a row total or column total to find the count for one variable regardless of the other.
- Use the grand total (bottom-right cell) to calculate probabilities or percentages of the whole group.
- Always check: the sum of the row totals must equal the sum of the column totals, and both must equal the grand total.
Worked example
80 students were asked to name their favourite sport from rugby, football, and cricket. Results were recorded by year group.
| Year group | Rugby | Football | Cricket | Row Total |
|---|---|---|---|---|
| Year 10 | 18 | 16 | 11 | 45 |
| Year 11 | 14 | 13 | 8 | 35 |
| Column Total | 32 | 29 | 19 | 80 |
Using this table you can answer questions such as:
- How many Year 10 students chose cricket? Row: Year 10, column: Cricket = 11.
- Which sport was most popular overall? Rugby with a column total of 32.
- What percentage of all students chose football? 29 out of 80 = 36.25%.
- Check: row totals 45 + 35 = 80; column totals 32 + 29 + 19 = 80. Both equal the grand total. ✓
Pictograms
In a pictogram, each symbol represents a fixed number of items stated in the key. Symbols can be whole or partial to represent values that are not exact multiples of the key value.
Each symbol represents a fixed count shown in the key.
Pictograms are quick to read but become impractical for large data sets or values that are not easy multiples of the key value.
Bar Charts
The bar chart below shows the number of vehicles of each brand recorded in a car park survey.
Bar chart: number of vehicles by brand (total = 20).
Key rules for bar charts
- All bars must be the same width.
- Leave equal gaps between bars for categorical and discrete data.
- The frequency axis must start at zero.
- Label both axes clearly, including units where relevant.
Pie Charts
A pie chart uses the same vehicle data (total = 20). To find each sector angle, use:
Sector angle = (frequency ÷ total) × 360°
Pie chart: vehicle brands as a proportion of the total.
Worked example: calculating sector angles
Total vehicles = 20. Each angle = (frequency ÷ 20) × 360.
(6 ÷ 20) × 360 = 108°
(4 ÷ 20) × 360 = 72°
(2 ÷ 20) × 360 = 36°
(3 ÷ 20) × 360 = 54°
(5 ÷ 20) × 360 = 90°
108+72+36+54+90 = 360° ✓
Always verify that your sector angles sum to exactly 360°.
Key Points
- Pie charts show proportion; bar charts show frequency.
- In a bar chart, the frequency axis must start at zero and all bars must be the same width.
- Pie chart sector angles must sum to 360°.
- A pictogram must always include a key.
- Two-way tables require row totals, column totals, and a grand total. All three must be consistent.
⚠️ Common Mistakes
- Frequency axis not starting at zero on a bar chart makes differences look exaggerated.
- Forgetting to check that pie chart angles sum to 360°.
- Unequal bar widths or missing gaps between bars on a bar chart.
- No key on a pictogram makes the diagram unreadable.
- Two-way table totals not matching: if row totals and column totals do not both equal the grand total, a cell value is wrong.
- Rounding errors in pie chart angles: carry full values through the calculation and only round the final angle.
Which Display to Use?
| Display Type | Best Used When... | Watch Out For |
|---|---|---|
| Two-Way Table | You have two grouping variables and need to compare combinations or find totals quickly | Row totals, column totals, and grand total must all be consistent |
| Pictogram | You want a simple visual impression; values are small whole numbers | Key must be shown; partial symbols are harder to draw accurately |
| Bar Chart | Comparing frequencies across categories or discrete values | Equal bar widths; axis starts at zero; equal gaps between bars |
| Pie Chart | Showing each category as a proportion of the whole | Sector angles must sum to 360°; label each sector or include a key |
Ready to test what you have learned? Work through the practice questions below.
Next Topic: Averages for Discrete Data →