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Teaching mathematics
Teaching mathematics

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3.1 Variables

You have seen that an indeterminate quantity can be thought of as a specific quantity that happens to be unknown (for now), or as one of several unknown quantities. Extending this idea leads to thinking of a quantity as a variable, that is, as a single object that can change, or vary in some way.

Variables can be discrete or continuous.

A discrete variable can take only certain values, and it would be nonsensical to choose a value between them. The position number of a sequence is an example of a discrete variable. A position number can only be a whole number. It would be nonsensical to talk about the ‘3 and a halfth’ term.

A continuous variable is one which can take any value. The nature of a variable may depend on how it is measured. One of the common variables that learners will meet in school is time. Time is usually a continuous variable, but we can make it discrete by taking daily, or hourly, aggregate measurements. You will return to this idea in Week 8 (Working with data).

Activity 7 Representing covariance

Timing: Allow 15 minutes

Look at the four pairs of variables below.

  1. Are the variables discrete or continuous?
  2. Informally, how do you visualise each pair of variables changing together?
    • Time in hours / Time in minutes

    • Age / Number of hours of sleep

    • Number of people sharing a box of 24 chocolates / How many chocolates each person gets

    • Your age / Your elder sibling’s age.

  3. Now watch the video below which shows different mathematical representations of the first example.
Download this video clip.Video player: Video 2 Different representations of covariance
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Video 2 Different representations of covariance
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Discussion

Time in hours is usually considered as a discrete variable since we only write whole numbers of hours (except perhaps half hours)

Time in minutes could be either discrete or continuous.

An age is discrete as you are likely to measure it in years or in years and months, but not with an accuracy of days or hours.

Number of people and chocolates are discrete variables.

You might have thought of graphs, or lines growing together, or imagined groups of chocolates.