Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- A graph of a quantitative variable shows its distribution: which values occur and how often.
- Dotplots, stem-and-leaf plots and histograms all keep the values in order, smallest to largest.
- They show frequency (a count) or relative frequency (count ÷ n).
- Dotplots and stem-and-leaf plots keep every value. A histogram keeps only the count in each bin.
Key relationships
| Display | How to build it | Must include |
|---|---|---|
| Dotplot | One dot per value above (or beside) a number line; stack equal or nearly equal values | Equal spacing, including values with no dots; axis label with units |
| Stem-and-leaf plot | Stem = first digit(s); leaf = next single digit; stems in a column, leaves in order | Every stem in the range (even empty ones); a key such as 3 | 8 = 38 kg |
| Split stems | Each stem written twice: leaves 0–4, then 5–9 | Same key rules |
| Histogram | Values grouped into ordered, equal-width bins; bar height = frequency or relative frequency | Touching bars; labelled axes, with the vertical scale starting at 0; a stated boundary rule (e.g. a ≤ x < b) |
| Relative frequency | frequency ÷ n | Relative frequencies add to 1 |
A frequency histogram and a relative frequency histogram with the same bins have the same shape. Only the vertical scale differs.
Assumptions and conventions
- The variable is quantitative: numbers with a natural order and meaningful distances.
- Bins are equal in width and cover every value. In these notes a value on a boundary goes in the bin on its right.
- A histogram may be drawn sideways, with bins on the vertical axis; the rules do not change.
- Changing the bin width can change how a histogram looks. Try more than one width and state the one you use.
Mistakes to avoid
- Gaps between histogram bars. That is a bar chart for categories.
- Uneven axis spacing on a dotplot, or skipping values with no dots.
- Missing empty stems, leaves out of order, or two-digit leaves.
- No key on a stem-and-leaf plot.
- Boundary values put in the wrong bin or counted twice.
- Unlabelled axes, or no units.
- Reading exact values off a histogram. It shows only bin counts.
Quick self-check
- A bin holds 6 of 30 values. What is its relative frequency? (6 ÷ 30 = 0.20)
- A stem-and-leaf plot has the key 7 | 3 = 73 kg. What does the row 8 | 0 4 4 show? (Three values: 80, 84 and 84 kg)
- A relative frequency histogram of 60 values has a bar of height 0.15. How many values are in that bin? (0.15 × 60 = 9)
- Bins are 20 ≤ x < 30 and 30 ≤ x < 40. Which bin does 30 go in? (30 ≤ x < 40)
Next: practice questions.