Glossary
Quartile
The three values that divide an ordered dataset into four equal parts. The first quartile (Q1, 25th percentile) separates the bottom 25%; the second quartile (Q2, the median) splits the data in half; the third quartile (Q3, 75th percentile) separates the top 25%. Quartiles und...
Definition
The three values that divide an ordered dataset into four equal parts. The first quartile (Q1, 25th percentile) separates the bottom 25%; the second quartile (Q2, the median) splits the data in half; the third quartile (Q3, 75th percentile) separates the top 25%. Quartiles underpin the interquartile range and box plots.
Why It Matters
Quartiles are among the most intuitive summary statistics because they convey both location and spread without assuming symmetry. The interquartile range (Q3 minus Q1) is a robust measure of dispersion that is resistant to outliers, making quartiles indispensable in exploratory data analysis and data quality checks.
Example
A human resources department analyses employee salaries and finds Q1 = $42,000, Q2 = $58,000, and Q3 = $79,000. The interquartile range is $37,000, meaning the middle 50% of employees earn between $42,000 and $79,000. Any employee earning below Q1 − 1.5 x IQR ($42,000 − $55,500) or above Q3 + 1.5 x IQR ($79,000 + $55,500) is flagged as a potential outlier.
Related Terms
Software Notes
- SPSS: Analyze > Descriptive Statistics > Explore; quartiles shown by default
- R:
quantile(x, probs = c(0.25, 0.50, 0.75)) - Stata:
summarize variable, detaildisplays quartiles alongside the median