Constructing and Selecting Standard Graphs

Choose the graph to suit the question

A graph makes selected features of data easier to see. The best choice depends on both the type of data and what you want to show. Monthly temperatures suggest a line chart because their sequence matters. Counts of people using different transport types suggest a bar chart because the categories are separate. Transport shares could instead be shown in a pie chart if the main purpose is to show parts of a whole.

Quantitative data are numerical. Counts, such as the number of vehicles, are discrete: there cannot be 3.5 vehicles in a count. Measurements, such as river depth, are continuous: values can fall anywhere within a range. Qualitative information describes qualities or categories. You can count responses in each category and graph those frequencies.

A good justification links the graph to the data: ‘A scattergraph is suitable because each river site has paired measurements of width and depth, and the aim is to investigate their relationship.’

Set up scales and plot accurately

Give a graph a descriptive title. Label each axis with the variable and its unit, such as ‘River depth (m)’. Choose scales that cover the data, use the available space sensibly and are easy to read. Equal distances on an axis must represent equal numerical changes. A scale of 0, 10, 20, 30 is regular; equally spaced labels of 0, 10, 30, 100 are not.

When axes and scales are already provided, first work out the value of one small division. For example, if the gap between 0 and 10 m contains five equal divisions, each division represents 2 m. A width of 6 m is therefore three divisions from zero.

For a coordinate pair, locate the horizontal value first, then the vertical value. Their intersection is the point to plot. Check each point against the original data before adding any lines.

Line charts show change through a sequence

A line chart is useful for showing change over time or distance. Put the ordered variable, such as time, on the horizontal axis and the measured variable on the vertical axis. Plot each pair of values and join neighbouring points in order.

For a temperature record of 8°C at 09:00, 12°C at 12:00 and 10°C at 15:00, the line rises and then falls. The connected points make that sequence clear. Keep time spacing proportional: a six-hour gap should occupy twice the horizontal distance of a three-hour gap.

The line shows the pattern between observations, but it does not mean that every intermediate value was measured. It also cannot explain why the temperature changed.

Bar charts compare separate categories

Use a bar chart to compare categories or separate counts, such as the number of pedestrians at different survey sites. Put categories on one axis and their values on the other. Draw bars of equal width with equal gaps between them. Their heights represent the values, so a frequency axis should normally begin at zero.

A pictogram offers another way to display counts. Repeated symbols represent a stated number of objects or events. For a pedestrian survey, if one symbol represents four people, 12 people require three symbols and six people require one and a half. Keep full symbols the same size and include a clear key. Pictograms are accessible, but small differences can be harder to show precisely.

Histograms group continuous measurements

A histogram shows the frequency of measurements within numerical intervals. For this course, construct histograms with equal class intervals. For example, river depths could be grouped into 0–less than 10 cm, 10–less than 20 cm and 20–less than 30 cm. These intervals all have a width of 10 cm and do not overlap.

Place interval boundaries along the horizontal axis and frequency on the vertical axis. Draw each bar across its whole interval, with its height showing the frequency. The bars touch because the intervals form a continuous numerical scale.

The distinction is not simply whether the values are numbers. A bar chart of survey sites compares separate categories; a histogram of depths groups continuous measurements. A histogram shows how observations are distributed, but grouping means you cannot recover every original measurement.

Pie charts and divided bars show parts of a whole

A pie chart represents a whole as a circle. Each sector represents one category’s share. Use it when the categories together make a meaningful total, such as all journeys in a transport survey.

Convert a category’s frequency into an angle using:

$$\text{sector angle} = \frac{\text{category frequency}}{\text{total frequency}} \times 360^\circ$$

If percentages are provided, use:

$$\text{sector angle} = \text{percentage} \times 3.6^\circ$$

In a survey of 40 journeys, 20 are by car, 12 on foot and eight by bus. Their shares are 50%, 30% and 20%, giving angles of 180°, 108° and 72°. Draw a circle, mark a starting radius, measure the angles with a protractor and distinguish the sectors with labels or a key. Together they fill 360°.

A divided bar splits one bar into sections representing the same categories. For a percentage divided bar, the whole bar represents 100%. On a 10 cm bar, the journey shares occupy 5 cm, 3 cm and 2 cm. Mark cumulative boundaries at 5 cm, 8 cm and 10 cm.

Pie charts emphasise each part’s share of the whole. Equal-length percentage divided bars can make it easier to compare the composition of several surveys. However, neither reveals different survey totals unless those totals are also stated. A frequency divided bar can instead show actual counts, with the total bar length representing the total frequency.

Scattergraphs show relationships between paired measurements

Choose a scattergraph when each observation has two numerical measurements, such as river width and depth at the same site. Put one variable on each axis and plot one point for every pair. Do not connect successive points: the sites are not being shown as a sequence.

Data for Plotting river width against depth

In this example, the pair (6 m, 0.4 m) means a site with a river width of 6 m and depth of 0.4 m. Locate 6 on the horizontal axis and 0.4 on the vertical axis to plot it.

A line of best fit, when required, follows the overall pattern with points reasonably balanced on either side. It need not pass through every point or through the origin. A rising pattern suggests positive correlation; a falling pattern suggests negative correlation. A scattered pattern without a clear direction suggests no correlation. A relationship alone does not prove that one variable causes the other.

Constructing a population pyramid

A population pyramid is suitable for population data organised by age group and sex. It shows structure, rather than just a population total.

Place age groups on the central vertical axis, with the youngest at the bottom and the oldest at the top. Draw horizontal bars extending to opposite sides for males and females. Label both sides clearly and use the same numerical scale on each side, increasing outwards from zero. The horizontal values may be numbers of people or percentages; follow the supplied data and axis labels.

For example, if an age group contains 6% males and 5% females, its bars extend to 6 on the male side and 5 on the female side. Repeat for each age group, keeping the age bands aligned. This allows the two sexes to be compared within the same age group without confusing the graph with a time series.

Match the graph to the data

• Line chart: change over ordered time or distance; join neighbouring points.
• Bar chart: compare separate categories or counts; equal-width bars with gaps.
• Pictogram: show counts with repeated symbols; include a numerical key.
• Histogram: frequencies of continuous data grouped into equal class intervals; bars touch.
• Pie chart: show categories as proportions of one whole.
• Divided bar: show a total split into categories; percentage bars total 100%.
• Scattergraph: show the relationship between paired numerical measurements; do not join points.
• Population pyramid: age groups centrally, youngest at the bottom; sex-specific bars on opposite sides with matching scales.

Essential construction checks

Use a title, labelled axes, units and regular scales. Read the value of each small division before plotting. For each point, locate the horizontal value and then the vertical value.

Proportion calculations

$$\text{sector angle} = \frac{\text{category frequency}}{\text{total frequency}} \times 360^\circ$$ $$\text{sector angle} = \text{percentage} \times 3.6^\circ$$ $$\text{divided-bar section length} = \frac{\text{percentage}}{100} \times \text{whole bar length}$$

Scattergraph patterns

Positive correlation rises; negative correlation falls; no correlation has no clear direction. A best-fit line follows the overall pattern. Correlation does not establish causation.