Interquartile Range
The spread of the middle 50% of the data.
Formula
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Example
If Q₁ = 20 and Q₃ = 35, the interquartile range is 35 − 20 = 15.
How it works
The interquartile range measures how wide the middle half of a dataset is by subtracting the first quartile from the third quartile. Since Q1 marks the 25th percentile and Q3 marks the 75th percentile, the difference Q3 − Q1 gives the spread of the central 50% of the values while ignoring extreme low and high outliers. This makes it a useful measure of variability when the data are skewed or contain unusually large or small values.
When to use it
Use the interquartile range when you want a resistant measure of spread for data like test scores, house prices, salaries, or biological measurements. It is especially helpful when comparing datasets that may have outliers or are not symmetrically distributed.
Worked example, step by step
A class’s quiz scores have Q1 = 62 and Q3 = 84. Use the formula: IQR = Q3 - Q1 Substitute the values: IQR = 84 - 62 Calculate: IQR = 22 So, the interquartile range is 22 points.
Common mistakes to avoid
- Subtracting Q1 from the median instead of from Q3
- Using the smallest and largest values instead of the quartiles
- Forgetting that IQR describes the middle 50% of the data, not the full range
Did You Know?
The interquartile range is the backbone of the box plot and a robust way to spot outliers.
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