Classifying statistical data

Maths · Statistics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Before you choose a chart or an average, you must know what kind of data you have. Qualitative (categorical) data is described in words, such as colour or favourite sport. Quantitative data is numerical.

Quantitative data is either discrete or continuous. Discrete data can only take separate values and is usually counted, such as the number of goals. Continuous data is measured and can take any value in a range, such as height, mass or time.

Large sets of data are often put into groups called class intervals. For continuous data the groups must have no gaps and no overlaps, so that every value fits into exactly one group.

Rules to remember

Qualitative (categorical) data: words or categories, e.g. eye colour.
Quantitative data: numbers. It is either discrete or continuous.
Discrete: counted, only separate values, e.g. number of pets. Continuous: measured, any value in a range, e.g. time.
Shoe size is discrete: only certain sizes exist, even though some are halves.
Groups for continuous data: 10 < x ≤ 20, 20 < x ≤ 30, and so on (no gaps, no overlaps).
Groups for discrete data can be written 0–4, 5–9, 10–14.
For qualitative data the only average that can be found is the mode.

Common mistake

Deciding by how big or how exact the numbers look. Ask "is it counted or measured?": the number of people in a city is discrete however large it is, and a race time is continuous even when it is rounded to a whole second.

Worked example

For each customer a shop records the time spent in the shop, the number of items bought and the method of payment. Classify each of the three sets of data.

Time spent is a number that is measured and can take any value, such as 7.4 minutes, so it is continuous quantitative data.
Number of items is counted and can only be 0, 1, 2, 3, ... so it is discrete quantitative data.
Method of payment (cash, card) is a category, not a number, so it is qualitative data.

Answer: Time: continuous. Number of items: discrete. Method of payment: qualitative.

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