Charts for Discrete and Time Series Data

Start by identifying what the values mean

A diagram should match the type of data. Discrete numerical data take separate, countable values. For example, a household might have 0, 1, 2 or 3 cars, but not 1.6 cars. If every value is listed separately, the data are also ungrouped.

Data collected in time order form a time series. Examples include a shop's sales each month or a town's temperature at midday each day. Here, the order of the observations matters: rearranging the values would destroy information about change over time.

Vertical line charts for discrete numerical data

A vertical line chart shows the frequency of each ungrouped discrete numerical value. The numerical outcomes go on the horizontal axis and frequency goes on the vertical axis. A thin vertical line rises from each observed value to its frequency.

Suppose a survey records the number of siblings of 20 pupils:

To construct the chart:

1. Label the horizontal axis Number of siblings and the vertical axis Frequency.
2. Mark the discrete values 0, 1, 2, 3 and 4 at equal intervals.
3. Choose an even vertical scale reaching at least the greatest frequency, 8.
4. Draw a thin vertical line at each value, with heights 3, 8, 6, 2 and 1 respectively.
5. Add a clear title.

The lines remain separate because the possible values are distinct. Do not join their tops: a joining line would suggest a meaningful progression through intermediate values. This is also why a vertical line chart differs from a time-series line graph.

Reading a vertical line chart

Read a frequency by moving from a numerical value up to the top of its line and then across to the frequency scale. In the siblings example, the line at 2 reaches 6, so six pupils have two siblings.

The tallest line identifies the mode. Here it is at 1, so one sibling is the modal number. Adding all the line heights gives the total frequency:

$3+8+6+2+1=20.$

A chart can also show the spread and shape of the data. Most of these results are concentrated around one or two siblings, while four siblings is relatively uncommon. Such conclusions must come from what the chart actually displays.

Organising a time series in a table

A time-series table places each time alongside its corresponding observation, normally in chronological order. Consider this record:

The headings should name the quantity and give its unit when one is needed. Regular time intervals make changes especially easy to compare, but irregular intervals can also be plotted provided their spacing on the time axis is accurate.

Constructing a time-series graph

Time always goes on the horizontal axis. The observed quantity goes on the vertical axis. Choose uniform scales that cover all the data, label both axes, include units and give the graph a title.

Plot each ordered pair, such as January at 42 and February at 46. Join consecutive points with straight line segments. The joining lines help the eye follow changes in time order; they do not prove that every intermediate value was observed.

Always check the finished graph against the table. Each row or column of data should produce exactly one plotted point, and each point should be above the correct time.

Interpreting change and trend

A time-series graph can show rises, falls, peaks, troughs and an overall trend. In the sales data, sales fluctuate: they fall from February to March and from May to June. Nevertheless, the later figures are generally higher than the earlier ones, so the overall trend is upward.

A strong description separates the overall direction from short-term fluctuations. “Sales increase overall, although there are small falls in March and June” is more informative than “the graph goes up and down”. Quote readings when the question asks for evidence, taking care to include the correct unit.

A repeated pattern at regular intervals may also be visible in a longer series. However, for this specification you need to comment on the general trend; moving averages and average seasonal trends are not tested.

Choosing an appropriate representation

Use the structure of the data to decide:

• Ungrouped discrete numerical data: use a vertical line chart when the separate numerical values and their frequencies need to be clear.
• Data recorded over time: use a time-series table and line graph so that order and change are visible.
• Categories: a bar chart or pictogram is usually suitable; a pie chart is useful for proportions of one whole.
• Grouped continuous data: a histogram may be appropriate, rather than a vertical line chart.

A table is best when exact values matter. A graph is often better for seeing a pattern quickly. The most attractive diagram is not necessarily the most suitable: the choice must preserve the meaning of the data.