Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- A bar chart shows one categorical variable with one bar per category. The bar’s height (or length) is the frequency or the relative frequency.
- A pie chart shows the same distribution as slices of a circle. Each slice’s share of the whole circle is its relative frequency, and all the slices together make up the whole.
- A frequency bar chart and a relative frequency bar chart of one data set have the same shape; only the axis scale differs.
- Graphs are evidence: a claim must quote values read from the graph and be stated in context.
- Tables, bar charts and pie charts can all compare two or more groups on the same categorical variable.
Key relationships
| You know | You want | Use |
|---|---|---|
| count, n | relative frequency | count ÷ n |
| relative frequency | slice angle | relative frequency × 360° |
| slice angle, n | count | (angle ÷ 360°) × n |
| relative frequency, n | count | relative frequency × n |
| all slice angles | a check | they add to 360° |
| two groups with different n | a fair comparison | compare relative frequencies |
Assumptions and conventions
- For a pie chart, every individual is in exactly one category and no category is left out.
- Bars are separate, of equal width, and the frequency axis starts at 0.
- Order the bars by size, or keep a natural order (for example, “Never, Sometimes, Often”) if there is one.
- Rounded percentages may total 99.9% or 100.1%. Say the difference is due to rounding.
Mistakes to avoid
- Comparing counts from groups of different sizes. Use proportions.
- “Most common” read as “most”. A majority needs more than 0.50.
- Using a percentage as an angle. 30% is 108°, not 30°.
- A pie chart for “tick all that apply” data. The parts add to more than the whole. Use a bar chart.
- An axis that does not start at 0, which exaggerates differences.
- Calling a bar chart “skewed”. Categories have no number-line order, so describe the most and least common categories instead.
- Reading a count from a proportion without n. You cannot.
Quick self-check
- A category has relative frequency 0.15. What is its slice angle? (0.15 × 360° = 54°)
- In a pie chart of 64 people, a slice has angle 90°. How many people is that? (90 ÷ 360 × 64 = 16 people)
- Group A (n = 500) has 150 people in a category; group B (n = 200) has 70. Which group has the larger proportion in it? (A: 0.30; B: 0.35, so B, even though its count is smaller)
Next: practice questions.