Quartile Calculator
Enter your data set below to instantly get Q1, the median, Q3, and the interquartile range.
What Are Quartiles?
Quartiles divide a sorted data set into four equal-sized groups. This calculator uses linear interpolation between ranks, the same method behind the percentile calculator, applied specifically at the 25th, 50th, and 75th percentiles.
Worked example
Data set: 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 (already sorted, n = 10)
Q1 rank = 0.25 × (10 − 1) = 2.25, between the 3rd value (36) and 4th value (39) → Q1 = 36 + 0.25 × (39 − 36) = 36.75
Median (50th percentile) = 40.5
Q3 rank = 0.75 × 9 = 6.75, between 42 and 43 → Q3 = 42 + 0.75 × (43 − 42) = 42.75
IQR = Q3 − Q1 = 42.75 − 36.75 = 6
Frequently Asked Questions
What are quartiles?
Quartiles split a sorted data set into four equal parts. Q1 is the value below which 25% of the data falls, Q2 is the median (50%), and Q3 is the value below which 75% falls.
What is the interquartile range (IQR)?
The IQR is Q3 minus Q1 — the range covered by the middle 50% of the data. It's a common way to measure spread while ignoring extreme outliers at either end.
How are quartiles used to find outliers?
A common rule flags any value more than 1.5 times the IQR below Q1 or above Q3 as an outlier. This is the same rule that determines the whiskers on a box plot.
How is this calculator different from the percentile calculator?
Quartiles are just three specific percentiles (25th, 50th, and 75th) bundled together. The percentile calculator finds any percentile you ask for, one at a time.
Related Calculators
- Standard Deviation Calculator — Statistics
- Percentile Calculator — Statistics
- Mean, Median, Mode Calculator — Statistics
- Variance Calculator — Statistics