Range vs Interquartile Range
Range and interquartile range both describe spread, but they answer different questions. Range uses only the minimum and maximum. Interquartile range focuses on the middle half of the data and resists outliers much better.
What is Range?
The range is the difference between the maximum and minimum values in a data set, giving the simplest measure of overall spread. It tells you the total span of the data from lowest to highest in a single number.
💡 Range tells you how spread out your data is from end to end. If the tallest kid is 5 feet and the shortest is 4 feet, the range is 1 foot - that's the 'stretch' of heights.
What is Interquartile Range (IQR)?
The interquartile range (IQR) is the range of the middle 50% of data, calculated as Q_3 - Q_1. It measures spread while ignoring the top and bottom 25% of values, making it resistant to outliers.
💡 IQR focuses on where most of the data lives, ignoring the extremes. If regular range is how far the outliers stretched, IQR is how wide the main crowd is. More resistant to outliers than range.
Key Differences
| Aspect | Range | Interquartile Range (IQR) |
|---|---|---|
| Values used | Only the minimum and maximum | The first and third quartiles |
| Sensitivity to outliers | Very sensitive | Much more resistant |
| What it measures | Total end-to-end spread | Spread of the middle 50% of the data |
| Best use | Quick rough span | Comparing typical spread when extremes may distort the picture |
⚠️ Where People Get Stuck
- • Thinking two datasets with the same range must have similar spread overall
- • Ignoring outliers that make the range look much larger than the typical spread
- • Using IQR without understanding quartiles first
- • Reporting only one spread measure without checking the data shape
A Simple Example
Dataset A is $1, 5, 5, 5, 9$ and dataset B is $1, 4, 5, 6, 9$.
Range
Both datasets have range = 8 because the minimum is 1 and the maximum is 9.
Interquartile Range (IQR)
The IQR distinguishes the middle spread: dataset A is more tightly clustered than dataset B even though the total range matches.
🎯 When to Use Which
Use range for a quick sense of the full span. Use interquartile range when you want a more stable description of typical spread, especially when outliers are present.
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