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Mathematical Requirements for Research Methods

The range and standard deviation

  • 3 things to know
  • Component 01

Overview

Recall questions on calculating and evaluating the range, what the standard deviation measures and how to calculate it, comparing conditions with different standard deviations, outliers, and reporting dispersion with central tendency.

What you need to know

Answer each one before you reveal it.

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Key term

A data set contains one extremely high outlier. Why may neither the range nor the standard deviation describe its spread well?

Key term

Find the range of the scores 14, 18, 22, 29 and 35.

Key term

What does the standard deviation measure?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Find the range of the scores 14, 18, 22, 29 and 35.

    Model answer

    The range is 21.

  2. 2

    State one strength and one weakness of the range.

    Model answer

    It is quick and easy to calculate, but it uses only the two most extreme scores and so ignores how the rest of the data is spread.

  3. 3

    What does the standard deviation measure?

    Model answer

    The average amount by which the scores in a set differ from their mean.

  4. 4

    The five scores 7, 7, 10, 13 and 13 have a mean of 10. Using the version of the formula that divides by n − 1, calculate the standard deviation.

    Model answer

    The squared deviations total 36, so dividing by 4 gives a variance of 9 and a standard deviation of 3.

  5. 5

    Outline the steps in calculating a standard deviation.

    Model answer

    Find the mean, subtract it from every score, square each of those differences, add the squares, divide by one less than the number of scores and take the square root.

  6. 6

    Two conditions have the same mean but one has a much larger standard deviation. What does this tell you?

    Model answer

    Participants in that condition performed far less consistently, with scores spread more widely around the same average.

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Range means the highest score minus the lowest score.
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