Five-Number Summary Calculator
Paste or type a list of numbers and the calculator returns Tukey's five-number summary — minimum, Q1, median, Q3 and maximum — plus the interquartile range, Tukey fences and any outliers.
Five-number summary
Min 1, Q1 3.5, Median 5, Q3 6.5, Max 11
- Minimum
- 1
- Q1 (25th percentile)
- 3.5
- Median (Q2, 50th percentile)
- 5
- Q3 (75th percentile)
- 6.5
- Maximum
- 11
- Interquartile range (IQR)
- 3
- Range
- 10
- Lower Tukey fence (Q1 − 1.5·IQR)
- -1
- Upper Tukey fence (Q3 + 1.5·IQR)
- 11
- Count (n)
- 8
No Tukey outliers (no values beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR). Quartiles use the exclusive method (OpenStax / Moore & McCabe): for an odd-length dataset the median itself is excluded from each half before taking that half's median.
How to use this calculator
Type or paste numbers into the input field. Separate them with commas, spaces, tabs or new lines — all work. The calculator returns the five-number summary as one headline, with each value broken out below alongside the interquartile range, the range, the Tukey fences (Q1 − 1.5·IQR and Q3 + 1.5·IQR) and a list of any outliers beyond those fences. Decimals and negative numbers are handled correctly. Unrecognised tokens are ignored and reported under the result.
How the calculation works
Sort the values in ascending order. The minimum is the first value and the maximum is the last. The median (Q2) is the middle value — for an even-length list it is the mean of the two middle values. To find Q1 and Q3, split the sorted data into a lower and an upper half: when the count is even the split is straight down the middle; when the count is odd the median itself is excluded from each half. Q1 is the median of the lower half and Q3 is the median of the upper half. The interquartile range is Q3 − Q1, and Tukey's fences at Q1 − 1.5·IQR and Q3 + 1.5·IQR flag potential outliers — values outside the fences. This is the "exclusive" / Moore & McCabe quartile method (the standard in OpenStax Introductory Statistics and Khan Academy); Tukey's original hinges differ slightly for odd-length samples.
Worked example
Take the dataset 1, 3, 4, 5, 5, 6, 7, 11 (eight values, already sorted). The minimum is 1 and the maximum is 11. The median is the mean of the two middle values, (5 + 5) ÷ 2 = 5. The lower half is 1, 3, 4, 5, so Q1 = (3 + 4) ÷ 2 = 3.5. The upper half is 5, 6, 7, 11, so Q3 = (6 + 7) ÷ 2 = 6.5. The interquartile range is 6.5 − 3.5 = 3, and Tukey's fences sit at 3.5 − 4.5 = −1 and 6.5 + 4.5 = 11. The value 11 sits exactly on the upper fence (not beyond it), so this dataset has no outliers under the 1.5·IQR rule. The five-number summary is (1, 3.5, 5, 6.5, 11).
Frequently asked questions
What is the five-number summary?
It is the set of five values that John Tukey proposed in Exploratory Data Analysis (1977) to describe a univariate dataset: the minimum, the first quartile (Q1, the 25th percentile), the median (the 50th percentile), the third quartile (Q3, the 75th percentile), and the maximum. Together they divide the data into four roughly equal groups and capture the spread, the centre, and the tails in a single compact summary. A box plot is the picture of a five-number summary — the box runs from Q1 to Q3 with a line at the median, and the whiskers extend out to the minimum and maximum (or, in modern variants, to the values just inside Tukey's fences).
Which quartile method does this calculator use?
The exclusive method, also known as Moore & McCabe's method — when the dataset has an odd number of values, the median itself is excluded from both halves before taking each half's median. This is the convention used in OpenStax Introductory Statistics, Khan Academy, most US college statistics textbooks, and Excel's QUARTILE.EXC function. There are other valid methods: Tukey's "hinges" include the median in both halves; Excel's QUARTILE.INC uses linear interpolation (the "C = 1" method) and is the default in NumPy; and there are at least nine numbered quantile types in R. They typically agree for even-length samples and disagree by small amounts for odd-length samples — the disagreement disappears as the dataset grows.
What does the interquartile range (IQR) tell me?
The IQR is Q3 − Q1, the width of the middle half of the data. It is a robust measure of spread: unlike the range (max − min) it ignores the two tails, so a single extreme value does not change it. It is the same units as the original data, which makes it easy to read. The IQR is also the box width on a box plot and the basis for Tukey's outlier rule.
How does the calculator decide what counts as an outlier?
It uses Tukey's 1.5·IQR rule: any value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR is flagged as an outlier. The two thresholds are called the lower and upper fences. The rule is a heuristic, not a definition — it tends to flag about 0.7% of values in a normal distribution as outliers, which is usually low enough to be useful and high enough to catch genuine anomalies. Some texts also draw "outer" fences at 3·IQR for "extreme" outliers; this calculator only shows the standard 1.5·IQR fences.
What if I only have one number, or all the numbers are identical?
With one value, all five summary statistics collapse to that single number — the minimum, Q1, median, Q3 and maximum are all the same, and the IQR and range are both zero. With multiple identical values you get the same result: zero IQR and zero range. The calculator reports the numbers honestly in those degenerate cases. With two distinct values, Q1 equals the smaller value and Q3 equals the larger one (each half has one element), and the median sits halfway between.
How does this differ from the mean and standard deviation?
The mean and standard deviation describe the average and the typical squared distance from it. The five-number summary describes the shape of the data instead: where the middle is, how wide the middle half is, and how far the tails extend. The summary is more robust — a single extreme outlier can swing the mean and inflate the standard deviation enormously, but it changes the median, Q1 and Q3 by at most one slot. For symmetric, bell-shaped data the two summaries tell similar stories; for skewed data or data with outliers the five-number summary is usually more informative.