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Categorical, Ordinal and Ranked Data

FoundationHigherAQAEdexcel

Practise Categorical, Ordinal and Ranked Data for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Data can be categorical (nominal), ordinal (ordered categories), or measured on interval and ratio scales.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Qualitative data divides further into categorical, ordinal and ranked data, and the distinction affects which averages can be used.

Categorical data has no natural order — eye colour, favourite subject, brand of phone. Only the mode is meaningful.

Ordinal data has a natural order but the gaps between categories are not necessarily equal. Exam grades, satisfaction ratings and finishing positions are ordinal. Because there is an order, the median can be found as well as the mode, but the mean cannot be calculated meaningfully. Ranked data assigns positions in order, and is a form of ordinal data used in rank correlation.

Revision notes

Categorical data

Data with no natural order, such as eye colour, favourite subject or type of transport.

The categories can be listed in any order without losing meaning. Only the mode is available as an average.

Ordinal data

Data with a natural order but not necessarily equal gaps between categories.

Examples: exam grades A to E, satisfaction ratings from poor to excellent, finishing positions in a race. The median can be found because the data can be put in order.

Ranked data

Data where items are assigned positions in order, such as 1st, 2nd, 3rd.

It is a form of ordinal data. Ranking is used in Spearman's rank correlation coefficient, where the actual values are replaced by their positions in order.

Key points

  • Categorical data has no natural order.
  • Only the mode is available for categorical data.
  • Ordinal data has a natural order.
  • Ordinal gaps are not necessarily equal.
  • The median can be found for ordinal data.
  • Ranked data assigns positions in order.

Worked examples

Example 1

State whether exam grades are categorical or ordinal data. [1 mark]

Working

Ordinalexam grades have a natural order from highest to lowest

Example 2

Explain why the median can be found for ordinal data but the mean cannot. [2 marks]

Working

Ordinal data can be placed in order, so the middle value can be identifiedexplain the median
but the gaps between categories are not necessarily equal, so the values cannot meaningfully be added and dividedexplain why the mean fails

Example 3

A survey records satisfaction as poor, fair, good or excellent. State the type of data. [1 mark]

Working

Ordinalthe categories have a natural order

Common mistakes

  • Treating ordinal data as fully numerical.

    The gaps between categories are not necessarily equal, so the mean is not meaningful.

  • Saying categorical data can be ordered.

    By definition it has no natural order.

  • Confusing ranked with quantitative.

    A rank is a position, not a measurement.

  • Finding a median of categorical data.

    Without an order there is no meaningful middle value.

Exam tips

  • Ask whether the categories have a natural order.
  • Remember only the mode works for categorical data.
  • Explain the ordinal mean problem through unequal gaps.
  • Link ranked data to Spearman's rank correlation.

Key terms

Categorical
Qualitative data with no natural order.
Ordinal
Qualitative data with a natural order.
Ranked
Data assigned positions in order.
Median
The middle value, available for ordinal data.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.