Pre-Algebra
Data and graphs
Measures of spread (range, IQR, MAD)
20 practice questions
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Theory + worked examples
Measures of Spread (Range, IQR, MAD)
Texas Pre-Algebra (TEKS) • Standard 6.12(C) • Data & Graphs
Measures of Spread (Range, IQR, MAD) is a topic in Data & Graphs in the Texas Essential Knowledge and Skills. It is aligned to Standard 6.12(C), which requires students to find and interpret measures of spread of a data set.
Spread measures variability: the range is max minus min, the IQR is \(Q_3-Q_1\), and the MAD is the average distance from the mean.
Theory
Measures of spread describe variability:
- Range: maximum minus minimum.
- IQR: \(Q_3-Q_1\), the middle-half spread.
- MAD: the average distance from the mean.
Larger spread means more variable data.
Small vs large spread.
Measures of spread.
Spread:
\[\text{range}=\max-\min,\quad \text{IQR}=Q_3-Q_1\]
MAD averages \(|x-\bar x|\).
How to measure spread
- Range: subtract the smallest from the largest.
- IQR: subtract \(Q_1\) from \(Q_3\).
- MAD: average the absolute deviations from the mean.
- Compare to judge variability.
Example 1 — Range
Find the range of \(3,7,9,12\).
Solution
Max minus min.
| \(12-3\) | \(=\) | \(9\) |
Example 2 — IQR
With \(Q_1=5,\ Q_3=11\), find the IQR.
Solution
Subtract.
| \(11-5\) | \(=\) | \(6\) |
Example 3 — MAD
Find the MAD of \(2,4,6\) (mean \(4\)).
Solution
Average \(|x-4|\).
| \(\dfrac{2+0+2}{3}\) | \(=\) | \(1.33\) |
Example 4 — Interpret
What does a larger spread mean?
Solution
The data are more variable.
Common pitfalls
IQR uses quartiles, not the extremes.
MAD uses absolute values.
Range is sensitive to outliers.
Frequently asked questions
What is the range?
Maximum minus minimum.
What is the IQR?
\(Q_3-Q_1\).
What is the MAD?
The average distance from the mean.
What does large spread mean?
More variable data.
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