Split any dataset into quarters — Q1, median, Q3, interquartile range, min, max, and range, with the data sorted for you. Free and exact.
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Quartiles divide an ordered dataset into four equal-frequency parts. The first quartile (Q1) marks the 25th percentile, the second quartile (Q2) is the median, and the third quartile (Q3) marks the 75th percentile. Together with the minimum and maximum, they form the five-number summary — the compact description behind every box plot you have ever seen.
Our free Quartile Calculator takes any list of numbers and returns Q1, Q2, Q3, the interquartile range (IQR), minimum, maximum, and range, with the sorted data shown so you can verify every step. It uses the widely taught Tukey hinge method: Q1 is the median of the lower half, Q3 the median of the upper half.
Why do quartiles matter? Because the mean and standard deviation can be dragged around by a single extreme value, while quartiles barely budge. Income data, house prices, and response times are routinely summarized with quartiles precisely because they describe the typical experience instead of letting outliers set the narrative.
Decimals and negative numbers are accepted, and blank entries between commas are ignored. The calculator needs at least four numbers because quartiles are undefined for tiny samples.
Quartiles are the three cut points that split ranked data into four groups of (approximately) equal size. Q1, the lower quartile, has about 25 percent of observations below it. Q2, the median, splits the data in half. Q3, the upper quartile, has about 75 percent below it. The middle 50 percent of the data — everything between Q1 and Q3 — is captured by the interquartile range, IQR = Q3 − Q1.
The IQR is one of the most useful spread measures in statistics because it describes the core of the data while ignoring the tails. Two datasets can have the same range but wildly different IQRs: imagine house prices in a town where most homes cost 200k–300k but one mansion costs 5M. The range is about 4.8M; the IQR is about 100k. Which number better describes ‘typical’ price variation? The IQR, by a mile.
There is more than one way to compute quartiles, and the methods can disagree slightly on small datasets. The main families are: Tukey’s hinges (median of each half, excluding the median itself when N is odd — used here), linear interpolation (the default in Excel’s QUARTILE.INC and NumPy), and exclusive/inclusive variants in Excel. For large datasets the differences vanish; for small ones, always note the method when comparing results across tools.
Quartiles power the box plot (box-and-whisker plot): the box spans Q1 to Q3 with a line at the median, and the whiskers extend to the most extreme non-outlier values. Points beyond 1.5 × IQR from the quartiles are conventionally flagged as outliers. This single picture — five numbers drawn as a box — lets analysts compare entire distributions at a glance, which is why quartiles appear in virtually every exploratory data analysis.
Finance offers another everyday example: investment returns are often quoted by quartile so clients see the typical outcome band rather than a mean distorted by one spectacular year. University admissions offices likewise report SAT score ranges as quartiles, giving applicants an honest picture of the middle fifty percent of admitted students instead of a single average that hides the spread.
Q2 = median of all data; Q1 = median of lower half; Q3 = median of upper half; IQR = Q3 − Q1
Sort the data. The median of the full set is Q2. Split the sorted data into a lower half and an upper half (excluding the median itself when N is odd). The median of the lower half is Q1; the median of the upper half is Q3. The interquartile range is Q3 minus Q1.
Worked by hand on 12, 15, 18, 21, 24, 27, 30, 33 (N = 8): sorted already. Median Q2 = (21 + 24)/2 = 22.5. Lower half: 12, 15, 18, 21 → Q1 = (15 + 18)/2 = 16.5. Upper half: 24, 27, 30, 33 → Q3 = (27 + 30)/2 = 28.5. IQR = 28.5 − 16.5 = 12. Minimum 12, maximum 33, range 21.
The five-number summary for this dataset is therefore 12, 16.5, 22.5, 28.5, 33 — everything a box plot needs, computed in under a minute.
Data: 7, 3, 9, 1, 5 (N = 5). Step 1: sort → 1, 3, 5, 7, 9.
Step 2: median Q2 = 5 (the middle value).
Step 3: lower half (excluding the median) = 1, 3 → Q1 = (1 + 3)/2 = 2. Upper half = 7, 9 → Q3 = (7 + 9)/2 = 8.
Step 4: IQR = 8 − 2 = 6. Five-number summary: 1, 2, 5, 8, 9.
Data: 10, 12, 14, 16, 18, 20, 200 (N = 7). Sorted already.
Q2 = 16 (middle). Lower half = 10, 12, 14 → Q1 = 12. Upper half = 18, 20, 200 → Q3 = 20.
IQR = 8. Note how the 200 barely affects Q1, Q2, Q3 — but the mean is 41.4, pulled far above every typical value. This is the robustness of quartiles in action.
Using Example 2: Q1 = 12, Q3 = 20, IQR = 8. Lower fence = 12 − 1.5 × 8 = 0. Upper fence = 20 + 1.5 × 8 = 32.
The value 200 exceeds the upper fence, so it is flagged as an outlier. In a box plot it would appear as a lone dot above the whisker — exactly the visual warning analysts rely on.
HR teams report salary bands as quartiles: Q1 is the entry-level zone, the median is the market midpoint, Q3 marks experienced hires. Candidates use these bands to judge offers — an offer at Q3 is strong regardless of what the average says, because averages are inflated by executive pay. Our calculator turns any salary survey list into these bands instantly.
Call centers track the quartiles of wait times: if Q3 is 4 minutes, three-quarters of callers wait less than that. Managers set targets on quartiles (‘Q3 under 3 minutes’) rather than averages because one disastrous hour should not define the metric. The IQR also reveals consistency — a small IQR means predictable service.
Quartiles split ordered data into four equal-frequency parts: Q1 (25th percentile), Q2/median (50th), Q3 (75th). The interquartile range IQR = Q3 − Q1 measures the spread of the middle 50% and is robust to outliers. This calculator uses Tukey’s hinges (median of each half). The five-number summary (min, Q1, median, Q3, max) underlies box plots; values beyond 1.5×IQR from the quartiles are conventional outlier fences.
Quartiles are three values that divide sorted data into four equal parts: Q1 (25% of data below), Q2/median (50% below), and Q3 (75% below). Together with the minimum and maximum they form the five-number summary used in box plots.
Sort the data, find the median (Q2), then take the median of the lower half as Q1 and the median of the upper half as Q3. Our calculator does this with the Tukey hinge method automatically.
The IQR is Q3 minus Q1 — the range covering the middle 50% of the data. It measures typical spread while ignoring extreme values, making it far more robust than the full range for skewed data.
Minimum, Q1, median (Q2), Q3, maximum. These five numbers describe a distribution’s center, spread, and extremes, and they are exactly what a box plot draws.
The standard rule flags values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as outliers. Our worked example shows a 200 in a dataset of teens being caught by this fence.
The mean is pulled by extreme values; quartiles are not. For skewed data like incomes or house prices, quartiles describe the typical experience while the mean can be wildly unrepresentative.
Yes, slightly, on small datasets — Tukey hinges, Excel’s interpolation, and inclusive/exclusive variants can disagree. On large datasets the differences are negligible. Always note the method when exact agreement matters.
Quartiles are specific percentiles: Q1 is the 25th percentile, Q2 the 50th, Q3 the 75th. Percentiles generalize the idea to any percentage, while quartiles are the four landmark divisions.
Cite this page as: Quartile Calculator — Sigma Calculator. https://sigmacalculator.net/statistics-calculators/quartile-calculator/
Last updated: October 11, 2026