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Quantile that divides a dataset or distribution into four equal-probability segments.
DESCRIPTION
Quartiles are the 25th (Q1), 50th (median, Q2), and 75th (Q3) percentiles that divide data into four equal parts. The interquartile range (IQR = Q3 − Q1) measures middle spread and supports robust outlier detection. Quartiles underpin box plots and five-number summaries for exploratory analysis. As with quantiles, computation methods vary across software; consistent definitions are important for comparability.
ALTERNATIVE DEFINITIONS
Wikipedia
A quartile is a type of quantile which divides the data into four equal parts.
Directly links quartiles to quantiles and equal partitioning.
NIST/SEMATECH e-Handbook
Quartiles divide a data set into four equal parts.
Focuses on descriptive statistics for ranked data sets.
RELATED TERMS
Quantile Median Interquartile Range Box Plot Percentile Order Statistic Descriptive Statistics Five-Number Summary
COMPETING TERMS
KNOWLEDGE AREAS
Mathematics Data Science Data Visualization
TARGET AUDIENCE
Data Analyst Data Scientist BI Specialist Data Steward
EXTERNAL SOURCES
- Wikipedia - Quartile
- NIST/SEMATECH e-Handbook - Quartiles and IQR explained
- Wolfram MathWorld - Formal definitions and properties
- pandas - API for computing quartiles
TOP QUESTIONS
How are Quartiles used in box plots?
Box plots show Q1, median (Q2), and Q3, with whiskers and outliers. They concisely summarize central tendency and dispersion.
Category: Example
What is the Interquartile Range (IQR)?
IQR equals Q3 minus Q1 and measures the spread of the middle 50% of data. It’s robust against outliers.
Category: Requirements
Do different tools compute Quartiles differently?
Yes. Software uses various interpolation rules for sample quartiles. Define and document your method for reproducibility.
Category: Mistakes
When should I rely on Quartiles instead of variance?
When outliers or non-normality distort variance. Quartiles and IQR provide robust spread measures without distributional assumptions.
Category: Relevancy
How do Quartiles help with outlier detection?
Commonly, points below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged as outliers in exploratory analysis.
Category: Application
Are Quartiles defined for continuous distributions?
Yes. They are the 0.25, 0.5, and 0.75 quantiles of the distribution’s CDF, not just sample statistics.
Category: Example
What is a five-number summary?
Minimum, Q1, median, Q3, and maximum summarize central tendency and spread. It’s a compact EDA tool.
Category: Example
How do sample size and Quartile stability relate?
Small samples yield noisy quartile estimates, especially at tails. Larger samples stabilize estimates and comparisons.
Category: Performance
How can Quartiles inform service SLOs?
Quartiles (and higher percentiles) summarize latency distributions. Q3 or higher percentiles can set performance targets beyond averages.
Category: Application