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Also known as: IQR, Midspread, H-spread, Middle 50%
Difference between the third and first quartiles, capturing the spread of the middle 50% of values.
DESCRIPTION
The interquartile range (IQR) measures statistical dispersion as Q3 − Q1, focusing on the central 50% of a distribution. It is robust to outliers and skewed data, making it a preferred spread metric in exploratory data analysis. IQR commonly appears in box plots to identify potential outliers using rules like 1.5×IQR. It complements mean and standard deviation by reducing sensitivity to extreme values. Analysts use IQR in quality control, anomaly detection, and comparative studies across groups.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, the interquartile range (IQR), also called the midspread, middle 50%, or H-spread, is a measure of statistical dispersion, being equal to the difference between the 75th and 25th percentiles.
Highlights common synonyms and defines IQR via percentiles.
NIST
The interquartile range is the difference between the third (upper) and first (lower) quartiles and measures the spread of the middle half of the data.
Emphasizes IQR as a robust spread measure centered on the middle half.
RELATED TERMS
Quartile Median Percentile Box Plot Outliers Variance Robust Statistics
COMPETING TERMS
Standard Deviation Range Median Absolute Deviation
RELATIONS
- Broader: Range
KNOWLEDGE AREAS
Mathematics Data Science Data Quality Data Visualization
TARGET AUDIENCE
Data Scientist Data Analyst BI Specialist Data Steward
EXTERNAL SOURCES
- Wikipedia - Interquartile range
- NIST - Official handbook entry on IQR
- Khan Academy - Tutorial on calculating IQR
- Penn State Eberly College of Science - Lesson covering quartiles and IQR
TOP QUESTIONS
Why is Interquartile Range useful in data analysis?
IQR is robust to outliers and skewness, capturing the central spread. It provides a stable dispersion measure when standard deviation is overly influenced by extreme values.
Category: Relevancy
How is Interquartile Range computed from a dataset?
Sort the data, compute Q1 (25th percentile) and Q3 (75th percentile), then subtract Q1 from Q3. The result is the IQR.
Category: How-to
How does Interquartile Range relate to box plots?
The box in a box plot spans from Q1 to Q3, so its height equals the IQR. Whisker and outlier rules often depend on IQR multiples.
Category: Example
When should Interquartile Range be preferred over standard deviation?
Prefer IQR with heavy-tailed or skewed distributions, or when outliers might distort standard deviation. It better reflects central variability
Category: Best practices
What is a common mistake when using Interquartile Range?
Confusing IQR with total range is common. IQR measures middle 50% spread, not the full spread from minimum to maximum.
Category: Mistakes
How does Interquartile Range assist in outlier detection?
The 1.5×IQR rule flags values below Q1−1.5×IQR or above Q3+1.5×IQR as potential outliers. It’s a simple, robust heuristic.
Category: How-to
Is Interquartile Range affected by linear scaling?
Yes. Multiplying data by a constant scales IQR by the same constant. Adding a constant does not change IQR.
Category: Concept
What are alternatives to Interquartile Range for robust dispersion?
Median Absolute Deviation is a robust alternative. Trimmed standard deviation and interdecile range are other options.
Category: Alternatives
How does sample size impact Interquartile Range estimation?
Small samples can yield unstable quartile estimates, affecting IQR. Larger samples provide more reliable percentile-based measures.
Category: Trade-off