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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.
Eight pebble lengths (mm) are 2, 4, 4, 4, 5, 5, 7 and 9. What is the standard deviation?
When is standard deviation more useful than the interquartile range?
Questions from this subtopic
Each one with the model answer underneath.
- 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
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
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
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
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
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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