Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- A full description has four parts: shape, centre, variability and unusual features.
- Every part is in context: the variable, the individuals and the units.
- In this topic, centre and spread are estimated from the graph. Exact calculations come in Topic 1.7.
- A graph can support or reject a claim when you quote counts or values from it.
Key relationships
| Feature | What you see on the graph | Word to use |
|---|---|---|
| Shape (symmetry) | Longer tail towards larger values | Skewed right (positively skewed) |
| Shape (symmetry) | Longer tail towards smaller values | Skewed left (negatively skewed) |
| Shape (symmetry) | Two halves roughly mirror images | Approximately symmetric |
| Shape (peaks) | One main peak | Unimodal |
| Shape (peaks) | Two clear peaks | Bimodal |
| Shape (peaks) | Bars or values about equally frequent, no clear peak | Approximately uniform |
| Unusual feature | Value unusually far from the rest | Possible outlier |
| Unusual feature | Stretch of the scale with no data | Gap |
| Unusual feature | Group of values close together, set apart by gaps | Cluster |
| Centre | Middle value of the ordered data (on a histogram, the bin that holds it) | Median (estimate) |
| Variability | Smallest to largest value, and where most values lie | Range; “most values between … and …” |
Assumptions and conventions
- The graph shows one quantitative variable measured in the same units.
- Say “approximately” symmetric or uniform: real data are never exact.
- On a histogram you cannot read individual values. Use bin edges and counts.
- Without a numerical rule, call an unusual value a possible outlier.
Mistakes to avoid
- Naming skew after the peak. A peak on the left with a long right tail is skewed right.
- Missing a part. Shape alone is not a description; include centre, spread and unusual features.
- No context or units. “Skewed right” alone earns little.
- Calling a cluster an outlier. A large group beyond a gap is a cluster.
- Claiming an exact median from a histogram. Name the bin that contains it.
- Judging a claim by appearance. Quote a count or percentage and compare it with the claim.
Quick self-check
- A histogram has its tallest bar near the right end and bars that slowly shrink towards the left. Name the shape. (Unimodal and skewed left: the longer tail is towards smaller values.)
- Six bins have frequencies 2, 9, 4, 1, 8, 3. Describe the number of peaks. (Bimodal: clear peaks in the 2nd bin (9) and the 5th bin (8).)
- Data (seconds): 12, 15, 18, 19, 21, 22, 22, 25, 47. Name any unusual features. (A gap from 26 to 46 seconds and a possible outlier at 47 seconds, which is 22 seconds above the next largest value.)
Next: practice questions.