Introduction
Stem-and-leaf diagrams and box-and-whisker plots are two of the most frequently tested data-display tools in 9709 PS1. Both preserve or summarise the actual data values, making it straightforward to extract medians, quartiles, and measures of spread — all of which are prerequisites for further statistical analysis. Examiners routinely award marks for correct construction, accurate reading of quartiles, and perceptive comparison of two data sets, so precision in every step is essential.
Core Concept
Stem-and-Leaf Diagrams
A stem-and-leaf diagram splits each data value into a stem (the leading digit(s)) and a leaf (the final digit). Every original value is retained, so the distribution's shape is visible while the raw data is still readable.
Rules for a valid diagram:
- State the key, e.g.
5 | 3 represents 53. - Order leaves in ascending order from the stem outward.
- Leaves are single digits only.
- Include a title.
A back-to-back stem-and-leaf diagram places two data sets on either side of a shared stem, with one set's leaves reading left and the other's reading right. This allows direct visual comparison of shape, centre, and spread.
Box-and-Whisker Plots
A box-and-whisker plot (box plot) displays the five-number summary of a data set:
| Statistic | Symbol | Meaning |
|---|---|---|
| Minimum | Smallest value | |
| Lower quartile | 25th percentile | |
| Median | 50th percentile | |
| Upper quartile | 75th percentile | |
| Maximum | Largest value |
The box spans to (the interquartile range, IQR), a vertical line marks , and whiskers extend to the minimum and maximum. Plots drawn on a scaled axis allow direct comparison of two data sets placed above one another.
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