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Mathematical Requirements for Research Methods

Median, mode and choosing a measure of central tendency

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  • Component 01

Overview

Recall questions on defining and calculating the median and mode, the only measure for nominal data, which measure uses every score, comparing mean and median with an outlier, and when the mean is most appropriate.

What you need to know

Answer each one before you reveal it.

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Numbers

For the scores 2, 3, 4, 5, 6, 7 and 43, explain which measure better represents the data set.

Numbers

A set of scores has a range of 24 and the lowest score is 7. What is the highest score?

Key term

Define the median.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define the median.

    Model answer

    The middle value when all the scores are placed in order of size.

  2. 2

    Six participants scored 5, 8, 8, 11, 14 and 20. Calculate the median.

    Model answer

    The two middle scores are 8 and 11, so the median is 9.5.

  3. 3

    Define the mode.

    Model answer

    The score that occurs most frequently in a set of data.

  4. 4

    Which measure of central tendency is the only one that can be used with nominal data, and why?

    Model answer

    The mode, because categories cannot be ordered or added, so only the most frequent category can be identified.

  5. 5

    Which measure of central tendency uses every score in the data set?

    Model answer

    The mean, since all the values are added together before dividing.

  6. 6

    Consider the scores 2, 3, 4, 5, 6, 7 and 43. Calculate the mean and the median.

    Model answer

    The total is 70 divided by seven scores, giving a mean of 10, while the median is the fourth value, which is 5.

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