Construct and interpret bar charts, pie charts, line graphs, histograms and stem-and-leaf diagrams, and choose an appropriate display

What this dot point is asking

SEAB wants you to construct and interpret the standard statistical diagrams, bar charts, pie charts, line graphs, histograms and stem-and-leaf diagrams, to read values off them, and to choose a display suited to the data. Good data handling turns a list of numbers into a clear picture.

The answer

Bar charts and line graphs

A bar chart uses bars of equal width whose heights show the frequency of each category, with gaps between bars for separate categories. A line graph joins plotted points and is best for showing a trend over time, such as temperature through a day.

Pie charts

A pie chart shows how a whole divides into parts, with each sector's angle proportional to its frequency. Since a full circle is $360^\circ$, the angle for a category is:

Histograms

A histogram displays grouped continuous data with bars touching, since the data is continuous. For equal class widths the bar height is the frequency; the area of each bar represents the frequency of that class.

Stem-and-leaf diagrams

A stem-and-leaf diagram keeps the actual data values while showing their shape. The stem is the leading digit (or digits) and each leaf the final digit. A key explains the place value, and the diagram makes the mode, range and median easy to read.

Reading a value back from a pie chart

Pie-chart questions run in both directions: as well as drawing a sector from a frequency, you often have to recover a frequency from a sector angle. Reverse the angle formula: the frequency is $\tfrac{\text{sector angle}}{360^\circ} \times \text{total}$. So a sector of $54^\circ$ in a pie chart of $200$ people represents $\tfrac{54}{360} \times 200 = 30$ people. The same proportion can be read as a fraction or percentage of the whole, since the sector angle, the fraction, and the frequency all carry the same proportion. Being fluent at converting between angle, fraction, and frequency is what these interpretation questions test.

Comparing two data sets with back-to-back stem-and-leaf

A back-to-back stem-and-leaf diagram shares one central column of stems, with one data set's leaves growing leftward and the other's rightward, so two groups can be compared side by side. Reading it, the leaves nearer the stem are the smaller digits in each direction, and the overall shape shows which group tends higher or is more spread out. This display keeps every original value while making a direct comparison easy, for instance contrasting two classes' test marks. Recognising when a comparison calls for a back-to-back diagram, rather than two separate ones, is a useful data-handling judgement.

Examples in context

Example 1. Survey results. A pie chart of how people travel to work shows at a glance which mode is most common, because the largest sector dominates the circle. It communicates proportions more vividly than a table.

Example 2. Tracking sales. A line graph of monthly sales reveals seasonal trends, peaks and dips that a bar chart of totals would hide. The connected line emphasises change over time.

Try this

Q1. A category represents $\dfrac{1}{4}$ of the data. State its pie-chart sector angle. [1 mark]

• Cue. $\dfrac{1}{4} \times 360^\circ = 90^\circ$.

Q2. State which diagram best shows the change in a city's population over 50 years. [1 mark]

• Cue. A line graph, since it shows a trend over time.

Q3. In a pie chart of $200$ people, a sector has angle $54^\circ$. How many people does it represent? [2 marks]

• Cue. $\dfrac{54^\circ}{360^\circ} \times 200 = 30$ people.