Interquartile Range
Spread of the middle 50% of the data.
Formula
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Robust measure of spread
How it works
The interquartile range measures how wide the middle half of a data set is by subtracting the first quartile from the third quartile. Since Q1 marks the 25th percentile and Q3 marks the 75th percentile, the formula IQR = Q3 - Q1 gives the distance between these two cut points, so it captures the spread of the central values while ignoring the most extreme 25% on each end. This makes it a useful measure of variability when outliers could distort the ordinary range.
When to use it
Use the IQR when you want a spread measure that is less affected by unusually high or low values, such as in income data, test scores with a few extreme results, or skewed distributions. It is especially helpful when comparing the consistency of two data sets whose extremes are not representative of the typical values.
Worked example, step by step
Data set: 4, 7, 8, 9, 10, 12, 15, 18, 21 Step 1: Find the first quartile, Q1 = 8 Step 2: Find the third quartile, Q3 = 15 Step 3: Subtract: IQR = Q3 - Q1 = 15 - 8 Step 4: IQR = 7 Final answer: The interquartile range is 7.
Common mistakes to avoid
- Using the largest and smallest values instead of Q3 and Q1
- Forgetting to sort the data before finding quartiles
- Mixing up IQR with the full range or with the median
Did You Know?
The interquartile range ignores the extreme 25% at each end, making it a robust measure used in box plots.
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