Collect data and make a table

Decide what one observation means

To investigate travel time to school, define the population, the measurement unit and the journey being measured. A sample of friends arriving early may under-represent late arrivals. A large sample does not automatically remove selection bias.

Use disjoint categories if each person is counted once. In a survey where people can select several favourite sports, the category counts may exceed the number of people. A pie chart of one whole is unsuitable unless its parts divide that whole without overlap.

Turn responses into a frequency table

For a practice survey, twelve pupils each record exactly one travel category: Walk, Bus or Cycle. Their responses, in order, are:

Walk, Bus, Walk, Cycle, Walk, Bus, Walk, Walk, Bus, Bus, Cycle, Walk.

Make a row for each category. Take one response at a time and add one to its category’s count. Mark each response as you use it, so none is missed or counted twice. The frequency is the number of observations in that category.

The category labels say what was recorded, and the frequency heading says what is counted. Check 6 + 4 + 2 = 12 against the number of responses. A matching total is useful, but still check that each response went into the correct row.

Check your understanding 1 Add new observations to the right rows

Four more pupils respond: Bus, Walk, Bus, Cycle. Update the frequency table and its total. Keep a separate row for every category rather than writing only a list of numbers.

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Walk now has 7 pupils, Bus 6 and Cycle 3, giving a total of 16. The four new observations add one to Walk, two to Bus and one to Cycle. Retain the category labels and the frequency unit, pupils. Each new pupil contributes once to the total.

Choose a display for the variable

Bar charts compare categories with separate bars; pictograms need an explicit key, including whether partial symbols are allowed. Line graphs show ordered observations, usually over time. Pie charts compare parts of a known whole. Dot diagrams can preserve individual values and show clusters or gaps.

For the original twelve responses, pie-chart counts 6, 4 and 2 give sector angles of 180°, 120° and 60°. Each angle is its category’s fraction of the whole multiplied by 360°. A half circle for a different total need not represent six people. Category proportions and group sizes are separate information.

Read the scale before comparing heights

A truncated bar-chart axis can exaggerate a small difference. A pictogram doubled in both height and width has four times the drawn area, not twice. Ask whether the visual encoding matches the actual numbers and whether the title states the sample and unit.

Check your understanding 2 A whole must have disjoint parts

In a class of 30, 20 pupils like football and 18 like swimming; some like both. Can these two counts be the only sectors of a pie chart of the class? Explain.

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No. They sum to 38 and overlap. A pie chart needs disjoint parts of the whole, for example football only, swimming only, both and neither, after those counts are known. A labelled bar chart can compare the two preference counts without claiming they partition the class.