This quartile calculator finds the five-number summary of any data set: minimum, first quartile (Q1), median (Q2), third quartile (Q3) and maximum — plus the interquartile range (IQR) and any outliers. Paste your numbers below.
What Are Quartiles?
Quartiles split sorted data into four equal parts. Q1 is the 25th percentile (a quarter of values fall below it), Q2 is the median, and Q3 is the 75th percentile. Together with the min and max they form the five-number summary behind every box plot. Unlike the mean and standard deviation, quartiles are robust: one wild outlier barely moves them. This calculator is part of our Statistics Calculators collection.
Worked Example (Verified)
Data: 85, 90, 78, 92, 88, 76, 95, 89 → sorted: 76, 78, 85, 88, 89, 90, 92, 95.
- Median (Q2) = (88 + 89) ÷ 2 = 88.5
- Q1 = median of lower half (76, 78, 85, 88) = 81.5
- Q3 = median of upper half (89, 90, 92, 95) = 91
- IQR = 91 − 81.5 = 9.5; outlier fences at 67.25 and 105.25 → no outliers
What the IQR Tells You
- The IQR is the spread of the middle 50% of your data — the core of the distribution, ignoring extremes.
- Outlier rule: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged (Tukey’s rule) — the calculator applies it automatically.
- Comparing IQRs compares consistency: two classes can share a median while one has twice the IQR — same typical score, wildly different consistency.
- For normally-distributed data, IQR ≈ 1.349 × the standard deviation from our Standard Deviation Calculator — a bridge between the two spread measures.
Quartile Methods (Why Answers Sometimes Differ)
There are several accepted quartile conventions (Tukey hinges, inclusive/exclusive percentile methods, Excel’s QUARTILE.INC vs QUARTILE.EXC). They agree on large data sets and differ slightly on small ones. This calculator uses Tukey’s hinges — the box-plot standard taught in most statistics courses. Whichever a course or tool uses, the interpretation of the five-number summary stays the same, and the underlying spread measure pairs with the Variance Calculator.
Related Tools
- Standard Deviation Calculator
- Variance Calculator
- Statistics Calculators — the full collection
Frequently Asked Questions
How do I find Q1 and Q3?
Sort the data. Q2 is the median. Q1 is the median of the lower half and Q3 the median of the upper half (Tukey’s method, used here).
What is the IQR?
The interquartile range: Q3 − Q1. It measures the spread of the middle half of the data and is resistant to outliers.
What counts as an outlier?
By Tukey’s rule, any value more than 1.5 × IQR below Q1 or above Q3. The calculator lists them for you.
Why does Excel give slightly different quartiles?
Excel’s QUARTILE.INC interpolates percentile positions differently from Tukey’s hinges. Both are legitimate conventions; differences shrink as data sets grow.
Quartiles vs. percentiles — same thing?
Quartiles are specific percentiles: Q1 = 25th, Q2 = 50th, Q3 = 75th percentile.
Is this quartile calculator free?
Yes — free, instant, no sign-up.