The interquartile range (IQR) is the range of the middle 50% of data, calculated as Q_3 - Q_1. IQR is a robust measure of spread.
Definition
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.
💡 Intuition
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.
🎯 Core Idea
The IQR measures the spread of the middle 50% of the data by subtracting Q1 from Q3. It ignores the top and bottom 25%, making it resistant to outliers.
Example
Formula
Notation
IQR stands for Interquartile Range. Q_1 is the 25th percentile and Q_3 is the 75th percentile. The 1.5 \times IQR rule defines the outlier fences.
🌟 Why It Matters
IQR is a robust measure of spread. It's used to identify outliers and compare group consistency.
💭 Hint When Stuck
First, find Q1 (the median of the lower half of data) and Q3 (the median of the upper half). Then subtract: IQR = Q3 - Q1. This tells you the span of the middle 50% of your data and is used to identify outliers beyond Q1 - 1.5*IQR or Q3 + 1.5*IQR.
Formal View
Related Concepts
Compare With Similar Concepts
🚧 Common Stuck Point
Students sometimes compute IQR as max minus min (that is the range). IQR specifically uses Q3 − Q1, not the overall extremes.
⚠️ Common Mistakes
- Confusing with range
- Calculating from min/max instead of Q_1/Q_3
- Forgetting it represents 50% of data
Go Deeper
Frequently Asked Questions
What is Interquartile Range (IQR) in Statistics?
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.
What is the Interquartile Range (IQR) formula?
When do you use Interquartile Range (IQR)?
First, find Q1 (the median of the lower half of data) and Q3 (the median of the upper half). Then subtract: IQR = Q3 - Q1. This tells you the span of the middle 50% of your data and is used to identify outliers beyond Q1 - 1.5*IQR or Q3 + 1.5*IQR.
Prerequisites
Next Steps
How Interquartile Range (IQR) Connects to Other Ideas
To understand interquartile range (iqr), you should first be comfortable with stat quartiles and stat range. Once you have a solid grasp of interquartile range (iqr), you can move on to stat box plot and outlier detection.