How this calculator works
Enter a list of numbers, separated by commas, spaces, or line breaks, and this calculator returns the five-number summary — minimum, first quartile (Q1), median, third quartile (Q3), and maximum — along with the interquartile range (IQR) and any outliers flagged using Tukey's fences.
There is more than one published way to calculate Q1 and Q3, and different tools can give slightly different answers for the same data. This calculator uses Tukey's hinges with the median included in both halves when the data set has an odd number of values (sometimes called the inclusive or "TI-83" method). Excel's QUARTILE.INC and PERCENTILE.INC functions use linear interpolation instead, which can produce different results — always check which method a source uses before comparing quartile values across tools.
The method used here
Median: the middle value of the sorted data (or the average of the two middle values for an even count)Q1: the median of the lower half of the sorted data, including the overall median in that half when the count is oddQ3: the median of the upper half of the sorted data, including the overall median in that half when the count is oddIQR = Q3 − Q1Tukey fences: lower = Q1 − 1.5 × IQR, upper = Q3 + 1.5 × IQRThis calculator names its method explicitly (Tukey's hinges, median-inclusive) because quartile conventions genuinely differ between tools — the same data set can produce different Q1/Q3 values in Excel, R, or a graphing calculator depending on which of at least three common methods is used.
Worked example: spotting an outlier
- Data set: 2, 3, 3, 4, 4, 4, 5, 5, 6, 50 (already sorted, 10 values).
- Median: the average of the 5th and 6th values, (4 + 4) ÷ 2 = 4.
- Lower half (first 5 values): 2, 3, 3, 4, 4 → Q1 = median = 3. Upper half (last 5 values): 4, 5, 5, 6, 50 → Q3 = median = 5.
- IQR = 5 − 3 = 2. Upper fence = 5 + 1.5 × 2 = 8. Since 50 is greater than 8, it is flagged as an outlier.
Frequently asked questions
Why do different calculators give different Q1 and Q3 values for the same data?
There are several published methods for computing quartiles from a finite data set, differing mainly in how they handle the median when the count is odd, and whether they interpolate between two data points or always land exactly on one. This calculator uses Tukey's hinges (median-inclusive); Excel's default QUARTILE.INC uses linear interpolation, which can give a different answer on the same data.
What counts as an outlier?
This calculator flags any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as an outlier — the standard "1.5 × IQR" rule popularized by statistician John Tukey. It's a useful rule of thumb, not a strict statistical test, and values just outside the fences aren't necessarily errors.
What is the interquartile range used for?
The IQR measures the spread of the middle 50% of the data and is less sensitive to extreme values than the full range (max − min). It's the basis for both the Tukey outlier fences and the box in a box-and-whisker plot.
Does the median-inclusion rule matter when there's an even number of values?
Only when the count is odd. This calculator's method includes the overall median in both the lower and upper half before taking each half's own median as Q1 and Q3, but with an even count the sorted list already splits into two equal halves with no single middle value to include — so Q1 and Q3 are simply the median of the lower half and the median of the upper half.
Does the order I enter the numbers matter?
No — this calculator sorts the values automatically before computing quartiles, so you can paste in a list in any order.