What the exam asks
On the digital exam in Bluebook, you will not draw graphs by hand, but you must know how they are constructed to identify errors, match datasets to graphs, and read them accurately:
- Calculate frequencies, relative frequencies (proportions or percentages), or sample sizes from a given dotplot, stem-and-leaf plot, or histogram.
- Determine which display correctly represents a given dataset or frequency table.
- Explain what information is preserved or lost when switching between displays (e.g., individual data values vs. binned intervals) or when changing a histogram’s bin width.
- Distinguish quantitative displays (histograms, dotplots, stemplots) from categorical displays (bar charts).
Core ideas
Quantitative vs. categorical displays
Displays for a quantitative variable use a numerical scale with a natural, unchangeable order. You cannot rearrange the horizontal axis of a dotplot or histogram, or the stems of a stem-and-leaf plot, without destroying the shape of the distribution. In contrast, bar charts display categorical variables: the bars are separated by spaces, and the categories can be reordered (unless ordinal) without changing the data’s meaning.
Comparing the three displays
| Display | How it is constructed | Keeps exact individual values? | Best for |
|---|---|---|---|
| Dotplot | A number line with one dot above the line for each observation. Equal values stack vertically with even spacing. | Yes (if the scale is precise). | Small to moderate datasets; seeing clusters and gaps quickly. |
| Stem-and-leaf plot (stemplot) | Each value is split into a stem (all but the final digit) and a leaf (the final single digit). Leaves are listed in increasing order out from the stem. Must include a key showing units and place value (e.g., ). | Yes. | Small to moderate datasets when you need both the distribution’s shape and exact numerical values. |
| Histogram | The numerical axis is divided into contiguous intervals (bins) of equal width. Touching vertical bars show the frequency (count) or relative frequency (proportion/percent) of values in each bin. | No—only shows how many values fall in each interval. | Moderate to large datasets; continuous data with many distinct values. |