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Bivariate and Multivariate Data

FoundationHigherAQAEdexcel

Understand Bivariate and Multivariate 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. Bivariate data record two variables per item and multivariate data record more than two, letting relationships be explored.

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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

Bivariate data consists of two variables measured on each item, allowing the relationship between them to be investigated.

Height and mass measured for each person is bivariate. It is represented on a scatter diagram, with one variable on each axis, and correlation between the variables can then be described.

Multivariate data has more than two variables measured on each item. Recording height, mass, age and shoe size for each person gives multivariate data. It cannot be shown on a single scatter diagram, so it is usually presented in a table, and pairs of variables are examined separately.

Revision notes

Bivariate data

Two variables measured on each item or individual.

Example: the height and mass of each person in a group. It is represented on a scatter diagram with one variable on each axis, and correlation can then be described.

Multivariate data

More than two variables measured on each item.

Example: height, mass, age and shoe size for each person. It cannot be shown on a single scatter diagram, so a table is used and pairs of variables are examined separately.

Why it matters

Bivariate data allows relationships between two quantities to be investigated.

This leads directly into correlation, lines of best fit and prediction, which form a substantial part of the course.

Key points

  • Bivariate data has two variables per item.
  • It is shown on a scatter diagram.
  • Correlation can be described from bivariate data.
  • Multivariate data has more than two variables.
  • Multivariate data is usually shown in a table.
  • Pairs of variables are examined separately.

Worked examples

Example 1

State what is meant by bivariate data. [1 mark]

Working

Data in which two variables are measured on each item or individualdefine the term

Example 2

A researcher records the height, mass and age of each person. State the type of data. [1 mark]

Working

Multivariatethree variables are recorded for each person

Example 3

Explain why multivariate data cannot be shown on a single scatter diagram. [2 marks]

Working

A scatter diagram has only two axes, so it can show only two variablesstate the limitation
so multivariate data must be shown in a table, with pairs of variables examined separatelyexplain the alternative

Common mistakes

  • Calling two separate lists of data bivariate.

    The two variables must be measured on the SAME items to be bivariate.

  • Saying multivariate means a large sample.

    It means more than two variables per item, not more items.

  • Trying to plot three variables on one scatter diagram.

    A scatter diagram has two axes and shows two variables.

  • Confusing bivariate with correlation.

    Bivariate describes the data; correlation describes the relationship within it.

Exam tips

  • Check the variables are measured on the same items.
  • Count the variables per item to classify the data.
  • Link bivariate data to scatter diagrams and correlation.
  • Remember multivariate needs a table.

Key terms

Bivariate
Two variables measured on each item.
Multivariate
More than two variables measured on each item.
Scatter diagram
A diagram showing bivariate data.
Correlation
A relationship between two variables.

Related topics

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