Five Number Summary Calculator – Min, Q1, Median, Q3, Max
The five-number summary is one of the most useful tools in descriptive statistics. Popularized by statistician John Tukey, it condenses a dataset into five values — the Minimum, First Quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum — that together describe the center, spread, and shape of a distribution without relying on the mean or standard deviation. Because it is built entirely from order statistics, it stays robust even when a dataset contains extreme values that would otherwise distort mean-based measures.
Why use a five-number summary?
Before running deeper statistical tests, analysts often want a quick sense of how a dataset is distributed: is it symmetric or skewed? Are there outliers? How wide is the "typical" range of values? The five-number summary answers all of these questions at a glance and is the exact data used to draw a box-and-whisker plot, making it the standard entry point for exploratory data analysis (EDA) in classrooms, dashboards, and research alike.
How the calculation works
The calculator first sorts your data in ascending order. The Minimum and Maximum are simply the first and last values in that sorted list. The Median is the middle value (or the average of the two middle values for an even count). Q1 and Q3 depend on the quartile method you select:
- Tukey Hinges (default): the data is split at the median into a lower half and an upper half; Q1 is the median of the lower half and Q3 is the median of the upper half. This is the classic convention used to draw most textbook box plots.
- Inclusive (Excel QUARTILE.INC): computes Q1 and Q3 using linear interpolation at position
(n − 1) × p, matching spreadsheet software. - Exclusive (Excel QUARTILE.EXC): interpolates at position
(n + 1) × p, which excludes the endpoints and needs at least 4 data points for a stable result.
Once Q1 and Q3 are known, the Interquartile Range is IQR = Q3 − Q1, representing the spread of the middle 50% of the data, and the Range is Max − Min, the total spread of the entire dataset.
Detecting outliers
The calculator flags outliers using Tukey's IQR fence rule: any value below Q1 − k × IQR or above Q3 + k × IQR is flagged, where k is your chosen fence multiplier. A multiplier of 1.5 is the standard "mild outlier" threshold, while 3.0 flags only extreme outliers. This same fence logic is what determines whisker length on a box plot — points beyond the fences are drawn as individual markers rather than extending the whisker.
Comparing multiple datasets
Add additional datasets to see their five-number summaries and box plots rendered side by side on a shared scale. This is especially useful for comparing groups — for example, test scores across two classes, delivery times across regions, or before/after measurements — since differences in median position, box width, and whisker length are immediately visible without doing any extra math.
Frequency table mode
If your data is already grouped into unique values with counts (for example, value = 40 occurring 3 times), switch to Frequency Table mode. The calculator expands the value/frequency pairs into a full sorted dataset internally before applying the same five-number summary logic, so results match what you would get from typing out every value by hand.
Accuracy and limitations
All calculations run entirely in your browser using standard floating-point arithmetic and well-established quartile formulas — no external statistics library is required. Because different quartile methods (Tukey, Inclusive, Exclusive) use different interpolation rules, Q1 and Q3 can shift slightly depending on which method you choose, especially for small datasets; this is expected and matches the same variation you would see between statistics textbooks or spreadsheet software.