S2.3StatisticsCore

Measures of Spread

An average alone doesn’t describe data — you also need to know how spread out it is. The range, interquartile range and interpercentile range each measure spread, with different sensitivity to extreme values.

20 min Video by Zeeshan Zamurred Measures of Location and Spread

Edexcel AS Level Maths: 2.3 Measures of SpreadWatch the full walkthrough before the notes below.

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What you'll be able to do

Calculate the range
Calculate the interquartile range (IQR)
Calculate an interpercentile range
Choose a suitable measure of spread

Range and interquartile range

The $range$ is simply the largest minus the smallest value — easy, but distorted by outliers. The $interquartile range$ (IQR) is $Q_{3} - Q_{1}$ , the spread of the middle 50%, and is resistant to outliers.

range = max - min, IQR = Q_{3} - Q_{1}

IQR ignores the extremes, so it is more robust.

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Answer

8

Interpercentile range

An $interpercentile range$ is the difference between two percentiles, e.g. the 10th to 90th percentile range, $P_{90} - P_{10}$ . It captures the spread of the central part of the data while trimming the extremes.

Choosing a measure

Use the range for a quick, simple spread; use the IQR or an interpercentile range when outliers would distort the picture — they focus on the bulk of the data.

Tip — Outliers around? Prefer the IQR or interpercentile range over the range.

Formula recap

range = max - min

Simplest spread (outlier-sensitive).

IQR = Q_{3} - Q_{1}

Middle 50% — robust.

P_{90} - P_{10}

An interpercentile range.

Common mistakes to avoid

Computing IQR as Q₁ − Q₃.

It is Q₃ − Q₁ (upper minus lower).

Using the range when there are clear outliers.

The range is dominated by extremes; use the IQR instead.

Key takeaways

Range = max − min (sensitive to outliers).
IQR = Q₃ − Q₁ — the middle 50%, robust to outliers.
Interpercentile ranges (e.g. P₉₀ − P₁₀) trim the extremes.

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