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Mathematical Requirements for Research Methods

Normal and skewed distributions

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Overview

Recall questions on the shape of normal distributions, the proportion of scores within one standard deviation, positively and negatively skewed distributions and the order of their averages, and why distribution matters.

What you need to know

Answer each one before you reveal it.

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Key term

Why does it matter whether a set of scores is normally distributed?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Describe the shape of a normal distribution.

    Model answer

    It is a symmetrical bell-shaped curve, with most scores clustered around the centre and progressively fewer towards each tail.

  2. 2

    A set of scores has a mean of 50, a median of 50 and a mode of 50. What does this suggest about the distribution?

    Model answer

    It suggests a symmetrical distribution such as the normal curve, since the three measures coincide only when the scores are spread evenly about the centre.

  3. 3

    Roughly what proportion of scores in a normal distribution lie within one standard deviation of the mean?

    Model answer

    About 68% of the scores.

  4. 4

    What is a skewed distribution?

    Model answer

    An asymmetrical distribution in which the scores bunch towards one end and a longer tail stretches out to the other.

  5. 5

    In a positively skewed distribution, where is the long tail and how are the three averages ordered?

    Model answer

    The tail stretches to the right, and the mode is lowest, the median in the middle and the mean highest.

  6. 6

    In a negatively skewed distribution, where is the long tail and how are the three averages ordered?

    Model answer

    The tail stretches to the left, and the mean is lowest, the median in the middle and the mode highest.

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