Quartile Calculator
Calculate the quartiles and interquartile range (IQR) of a data set — useful for understanding data spread and outliers.
What quartiles tell you about your data
Quartiles split sorted data into four equal groups. Q1 (the 25th percentile) marks the point below which a quarter of the data falls, Q2 (the median) marks the halfway point, and Q3 (the 75th percentile) marks the point below which three-quarters of the data falls.
The interquartile range (IQR), the distance between Q1 and Q3, captures the spread of the middle 50% of your data — it's a more outlier-resistant measure of spread than the full range (max minus min), since it ignores extreme values at either end.
Using IQR to spot outliers
A common rule of thumb flags any value more than 1.5 times the IQR below Q1 or above Q3 as a potential outlier — this method is widely used in statistics (it's the basis for the whiskers on a standard box plot) because it doesn't rely on assuming a normal distribution the way some other outlier detection methods do.
Different statistical software and textbooks sometimes use slightly different methods for calculating quartiles on small data sets (this calculator uses a common median-based split method) — for large data sets the differences between methods become negligible, but for small samples, results can vary slightly by method.
Frequently asked questions
Why might my quartile results differ slightly from another calculator?
There are several accepted methods for calculating quartiles, particularly for small or even-sized data sets, and different tools sometimes default to different conventions — this calculator uses a common median-based split method, but results can vary slightly by method for small samples.
How is IQR used to detect outliers?
A common rule flags values more than 1.5 times the IQR below Q1 or above Q3 as potential outliers — this method is the basis for the whiskers shown on a standard box plot.