Bar Charts, Pie Charts and Pictograms
The most straightforward statistics topic — but it contains one calculation students reliably get wrong (pie chart angles) and one question type that catches people out (criticising a misleading diagram).
1. Bar charts
- Equal bar widths, with gaps between them
- Frequency on the vertical axis
- Both axes labelled, and the chart titled
The y-axis must start at ZERO. A bar chart starting at 30 exaggerates the differences between bars and is misleading — this is the most commonly examined criticism.
Compound and dual bar charts compare categories side by side, and need a key.
Reading them: check what one gridline is worth before reading any bar — the scale is rarely one square per unit.
2. Pie charts
The whole circle is 360°, representing the total.
Drawing one
Angle = (frequency ÷ total) × 360°
Example: 30 students — 12 walk, 10 cycle, 8 take the bus.
| Method | Angle |
|---|---|
| Walk | (12/30) × 360 = 144° |
| Cycle | (10/30) × 360 = 120° |
| Bus | (8/30) × 360 = 96° |
Check: 144 + 120 + 96 = 360° ✓
Always check your angles sum to 360°. It catches nearly every arithmetic error in one line, and takes seconds.
A useful shortcut: find the degrees per item first — here 360 ÷ 30 = 12° per student — then multiply by each frequency. Tutors used this method, and it is quicker when several categories share the same total.
Divide by the TOTAL, not by the number of categories. Dividing 360 by 3 because there are three categories is wrong unless the categories happen to be equal.
Drawing: use a protractor, measure each angle from the previous radius, and label every sector.
Reading one — working backwards
Frequency = (angle ÷ 360) × total
Example: a sector of 72° in a pie chart representing 200 people:
- (72/360) × 200 = 40 people
You cannot find actual frequencies from a pie chart without knowing the total. A pie chart shows proportions only. If two pie charts have different totals, a bigger sector angle does not guarantee a bigger frequency — a favourite exam question.
“Show that 75 students chose the museum” means prove it with working — write the calculation, not just the answer.
3. Pictograms
A picture or symbol represents a number of items, given by the key.
Always read the key first. If one symbol = 3 cars, then 4 symbols = 12 cars, not 4. Misreading the key was a documented error, and it invalidates everything that follows.
Part symbols represent fractions — half a symbol with a key of 4 means 2.
When drawing: keep symbols the same size, use the key consistently, and include the key.
4. Frequency polygons
Plot the midpoint of each class against its frequency, and join the points with straight lines.
Use midpoints, not upper or lower bounds — that is the difference from a cumulative frequency graph, which uses upper bounds.
5. Criticising a diagram
A common question shows a badly drawn chart and asks what is wrong. Look for:
- The y-axis does not start at zero — exaggerates differences
- No labels on the axes
- No title
- Missing key on a pictogram or compound bar chart
- Unequal bar widths or unequal gaps
- Non-linear scale — uneven gaps between numbers
- 3D effects distorting the comparison
Be specific, and say WHY it misleads. “The y-axis starts at 30 instead of 0, which makes the difference between the bars look far larger than it is” earns the mark; “the graph is wrong” does not. Tutors flagged this repeatedly — vague answers scored nothing.
Name the actual missing element. Saying “it needs percentages” when the real fault is a missing y-axis label was a recorded error. Read the diagram carefully and identify precisely what is absent.
6. Choosing the right diagram
| Use | When |
|---|---|
| Bar chart | comparing frequencies of categories |
| Pie chart | showing proportions of a whole |
| Pictogram | simple, visual comparisons |
| Histogram | continuous data with unequal class widths |
| Scatter diagram | relationship between two variables |
7. Mistakes that cost marks
Dividing 360 by the number of categories instead of the total.
Angles that don’t sum to 360°.
Reading frequencies off a pie chart without the total.
Comparing sector sizes across pie charts with different totals.
Misreading a pictogram key.
Omitting the key, labels or title.
Starting the y-axis above zero.
Using upper bounds instead of midpoints for a frequency polygon.
Vague criticism of a misleading graph.
Not simplifying a ratio when asked.
Frequently asked questions
How do I calculate a pie chart angle? (frequency ÷ total) × 360°.
How do I check my pie chart? The angles must add to 360°.
How do I find a frequency from a pie chart? (angle ÷ 360) × total — you must know the total.
Can I compare two pie charts directly? Only by proportion. A larger sector doesn’t mean a larger frequency unless the totals are equal.
What does a pictogram key tell me? How many items one symbol represents — always read it first.
Why must a bar chart’s y-axis start at zero? Otherwise the differences between bars are exaggerated, making the chart misleading.
What’s the difference between a bar chart and a histogram? Bar charts show categories with gaps; histograms show continuous data with no gaps and use area for frequency.
What do I plot for a frequency polygon? The midpoint of each class against its frequency.
Quick revision checklist
- I can draw a bar chart with equal widths, gaps and labels
- I know the y-axis must start at zero
- I can calculate pie chart angles with (frequency ÷ total) × 360
- I can use the “degrees per item” shortcut
- I check my angles total 360°
- I can work backwards from an angle to a frequency
- I know a pie chart shows proportions, not amounts
- I always read the pictogram key first
- I can interpret part symbols
- I plot midpoints for a frequency polygon
- I can criticise a misleading diagram specifically
- I can choose the right diagram for a given data type
These notes cover bar charts, pie charts and pictograms in the Cambridge IGCSE Mathematics (0580) syllabus, and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Maths lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus for your own exam series.
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