The interquartile range (IQR) is Q3 - Q1 — the spread of the middle 50% of the data, resistant to outliers. IQR is the standard spread measure for skewed or outlier-heavy data, and it defines the "fences" beyond which data points are classified as outliers in a box plot.
Definition
The interquartile range (IQR) is Q3 - Q1 — the spread of the middle 50% of the data, resistant to outliers.
💡 Intuition
The IQR ignores the extreme 25% on each end, capturing only the spread of the central bulk of data — making it robust when outliers inflate the regular range.
🎯 Core Idea
IQR is resistant to outliers—extreme values don't affect it.
Example
Formula
Notation
\text{IQR} = Q_3 - Q_1; the middle 50\% of the data
🌟 Why It Matters
IQR is the standard spread measure for skewed or outlier-heavy data, and it defines the "fences" beyond which data points are classified as outliers in a box plot.
💭 Hint When Stuck
Find Q1 and Q3 first. Then just subtract: IQR = Q3 - Q1. This tells you the spread of the middle 50% of data.
Formal View
See Also
🚧 Common Stuck Point
Outliers are typically defined as values more than 1.5 \times \text{IQR} from Q1 or Q3.
⚠️ Common Mistakes
- Computing IQR as Q1 - Q3 instead of Q3 - Q1 — IQR must be positive
- Confusing IQR with range — range uses min and max, IQR uses Q1 and Q3
- Using IQR alone to describe the data without reporting the median — IQR measures spread but not center
Go Deeper
Frequently Asked Questions
What is Interquartile Range in Math?
The interquartile range (IQR) is Q3 - Q1 — the spread of the middle 50% of the data, resistant to outliers.
Why is Interquartile Range important?
IQR is the standard spread measure for skewed or outlier-heavy data, and it defines the "fences" beyond which data points are classified as outliers in a box plot.
What do students usually get wrong about Interquartile Range?
Outliers are typically defined as values more than 1.5 \times \text{IQR} from Q1 or Q3.
What should I learn before Interquartile Range?
Before studying Interquartile Range, you should understand: quartiles.
Cross-Subject Connections
Visualization
StaticVisual representation of Interquartile Range