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Measures of dispersion: range, interquartile range and standard deviation

  • 3 things to know
  • Paper 2

Overview

Dispersion diagrams and what a measure of dispersion shows, the range, interquartile range and standard deviation with a worked example on pebble lengths, and when standard deviation is more useful than the interquartile range.

What you need to know

Answer each one before you reveal it.

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Process

Eight pebble lengths (mm) are 2, 4, 4, 4, 5, 5, 7 and 9. What are the range and the interquartile range?

Process

Eight pebble lengths (mm) are 2, 4, 4, 4, 5, 5, 7 and 9. What is the standard deviation?

Process

When is standard deviation more useful than the interquartile range?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is a dispersion diagram?

    Model answer

    A graph in which each value in a dataset is plotted as a dot against a vertical scale, showing the spread and clustering of the data and making the median and quartiles easy to find.

  2. 2

    What does a measure of dispersion show?

    Model answer

    How spread out the values in a dataset are around the average, which shows whether the average is typical of the data.

  3. 3

    What is the range, and what is its main limitation?

    Model answer

    The difference between the highest and lowest values; it is easy to calculate but is distorted by a single extreme value.

  4. 4

    What is the interquartile range, and why is it often better than the range?

    Model answer

    The difference between the upper quartile and the lower quartile, covering the middle 50% of the data, so it is not affected by extreme values.

  5. 5

    What is standard deviation?

    Model answer

    A measure of the average spread of values around the mean, calculated as the square root of Σ(x − x̄)² ÷ n (some texts divide by n − 1 for a sample); a low value means the data are clustered closely around the mean.

  6. 6

    Eight pebble lengths (mm) are 2, 4, 4, 4, 5, 5, 7 and 9. What are the range and the interquartile range?

    Model answer

    The range is 9 − 2 = 7 mm; the lower quartile is 4 and the upper quartile is 6 (the medians of each half of the data), so the interquartile range is 6 − 4 = 2 mm.

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