Five-Number Summary Calculator

Reviewed by CalcMulti Editorial Team·Last updated: February 2026·← Statistics Hub

The five-number summary describes the distribution of a dataset using five key values: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Together they reveal the centre, spread, and skewness of your data — and are the foundation of a box-and-whisker plot.

Paste your numbers (comma, space, or newline separated) to instantly compute all five values plus the interquartile range (IQR) and Tukey's outlier fences.

Unlike the mean and standard deviation, the five-number summary makes no assumption about the shape of your distribution. It is a non-parametric description — meaning it works equally well for symmetric bell curves, right-skewed income data, left-skewed test scores, and bimodal distributions. When a dataset contains outliers or follows a non-normal pattern, the five-number summary is usually more informative than mean ± SD because extreme values cannot distort the quartiles.

Reading skewness from the five numbers is straightforward: compare the gap between Q1 and the median with the gap between the median and Q3. If the lower gap is smaller (Median − Q1 < Q3 − Median), the data is right-skewed with a longer upper tail. If the lower gap is larger, the data is left-skewed. Equal gaps suggest approximate symmetry. Similarly, compare the whisker lengths: a longer upper whisker signals a right tail, a longer lower whisker signals a left tail.

Common applications include academic research (summarising test score distributions across classrooms), clinical studies (summarising patient age, weight, or biomarker levels that may be skewed), business analytics (reporting revenue or customer lifetime value where a few large accounts skew the mean), and quality control (tracking production measurements with occasional defects as outliers). Any time you need a quick, honest snapshot of a dataset without fitting a model, the five-number summary is the right tool.

Worked example: consider a dataset of 10 exam scores: 45, 52, 58, 63, 68, 72, 76, 81, 90, 97. Sorted, these give Min = 45, Q1 = 57.25 (between 3rd and 4th values), Median = 70.0 (average of 5th and 6th), Q3 = 80.25 (between 7th and 8th), Max = 97. IQR = 80.25 − 57.25 = 23.0. Lower fence = 57.25 − 34.5 = 22.75; upper fence = 80.25 + 34.5 = 114.75. No values fall outside the fences, so there are no outliers. The gap above the median (Q3 − Med = 10.25) is slightly larger than below (Med − Q1 = 12.75), suggesting a mild left skew in the score distribution.

Comparing two datasets side by side using five-number summaries is one of the most effective exploratory techniques in statistics. Suppose Class A has scores: Min 40, Q1 55, Med 68, Q3 78, Max 95, and Class B has Min 50, Q1 65, Med 72, Q3 82, Max 92. The median is similar (68 vs 72), but Class A has a wider IQR (23 vs 17), meaning more spread in the middle 50%. Class A also has a lower minimum, suggesting a tail of struggling students. A back-to-back box plot of these two five-number summaries immediately makes these patterns visible in a way that comparing only means (e.g., both might have mean ≈ 70) would completely obscure.

For reporting purposes, the five-number summary can be compressed into a single line: the notation [Min, Q1, Med, Q3, Max] with the IQR stated separately. In academic papers using APA style, this might appear as: "The distribution of response times was right-skewed (Mdn = 320 ms, IQR = 145 ms, range = 180–890 ms)." In business dashboards, quartile widgets give executives an instant feel for both the typical value (median) and the variability (IQR). When presenting raw data is not possible due to privacy constraints, the five-number summary conveys distribution shape with no individual data points exposed.