Choosing a Representation
There is rarely one display for every job. Choose the display that answers the question while losing as little useful information as possible.
bar chart
Use: categories or discrete values
+ quick comparison
− does not retain every raw value
stem-and-leaf
Use: a small numerical data set
+ retains every value
− becomes crowded with many values
histogram
Use: grouped continuous data
+ shows shape and crowding
− grouping loses individual values
cumulative-frequency graph
Use: grouped continuous data
+ reads totals and percentiles
− values between plotted points are estimates
Match the display to the job
| Display | Use it when you need to… |
|---|---|
| pictogram | communicate simple category counts to a general audience |
| bar chart | compare categories or ungrouped discrete values |
| pie chart | show how categories divide a whole |
| stem-and-leaf | show a small numerical data set and keep every value |
| histogram | show the shape of grouped continuous data |
| cumulative-frequency graph | read totals below thresholds or percentiles |
A vertical-line chart is also suitable for ungrouped discrete data: each allowed value has a line whose height shows its frequency. Box-and-whisker plots are taught in Chapter 3; they give a compact five-number summary, but they do not retain every raw value.
Explain what the display reveals or loses
- A stem-and-leaf diagram keeps the raw values, so you can recover the data. It becomes crowded for a large data set.
- Grouping makes the overall shape easier to see, but the individual values are lost.
- A histogram shows where continuous data are concentrated. A cumulative-frequency graph is better for counts below a value and percentiles.
Common mistake
Now you try
Choose a display and give one reason for each situation.
(a) Compare the exact test scores of two classes of 12 students.
(b) Show the shape of 500 measured journey times grouped into unequal intervals.
(c) Estimate how many of those journeys took less than a chosen time.
Show worked answer
(a) A back-to-back stem-and-leaf diagram: it compares the two small sets on one scale and retains every score. (b) A histogram: it shows grouped continuous data and handles unequal widths with frequency density. (c) A cumulative-frequency graph: it gives the running total below a time.