5-Number Summary Calculator — Box Plot Statistics
Paste or type your data set (numbers separated by commas, spaces, or new lines) to instantly get the five-number summary — minimum, Q1, median, Q3, maximum — plus IQR, range, and Tukey outlier fences.
Middle value of the sorted data — the central tendency measure
- 1
Count
1010 values sorted from 3 to 21. - 2
Q1 (lower quartile)
6 - 3
Q3 (upper quartile)
14 - 4
Median (Q2)
(8 + 12) ÷ 2 = 10
How does this calculator work?
The 5-number summary: min, Q1, median (Q2), Q3, max — plus IQR = Q3 − Q1 and range = max − min. Uses the exclusive (Tukey) method. Outlier fences: Q1 − 1.5·IQR and Q3 + 1.5·IQR. Paste any numeric data set to get all five values and the box-plot segmentsinstantly.
Formula
How this is calculated
The five-number summary describes a data set with five key statistics drawn from a sorted list. The minimum and maximum are the smallest and largest values. The median (Q2) is the middle value — or the mean of the two middle values when the count is even. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half.
This calculator uses the exclusive (Tukey) method: when the total number of values is odd, the overall median is excluded from both halves before computing Q1 and Q3. This is the method used by most statistical textbooks and the default in R. The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of the data.
Tukey's outlier fences extend 1.5 × IQR beyond Q1 and Q3. Values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR are flagged as potential outliers (mild outliers; 3 × IQR is used for extreme outliers). These five numbers are exactly what a box-and-whisker plot draws, making this calculator the first step in creating a box plot from scratch.
Frequently asked questions
The five-number summary (min, Q1, median, Q3, max) is the foundation of a box-and-whisker plot. It describes the spread, center, and skew of a data set without assuming a normal distribution, making it robust to outliers. It is widely used in descriptive statistics, exploratory data analysis, and data visualization.
It uses the exclusive (Tukey) method: when the count is odd, the overall median is not included in either half when computing Q1 and Q3. This differs from the inclusive method (used in some textbooks and Excel's QUARTILE.INC) which includes the median in both halves. Results may differ slightly between methods.
Tukey fences are calculated as Q1 − 1.5·IQR (lower) and Q3 + 1.5·IQR (upper). Any value beyond these fences is considered a mild outlier; values beyond Q1 − 3·IQR or Q3 + 3·IQR are extreme outliers. This rule is the standard outlier definition used in box plots.
Also known as
TG we-Calculate Editorial Team. (2026). 5-Number Summary Calculator — Box Plot Statistics [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/5-number-summary-calculator
TG we-Calculate Editorial Team. "5-Number Summary Calculator — Box Plot Statistics." TG we-Calculate. 2026. https://we-calculate.com/calculator/5-number-summary-calculator.
TG we-Calculate Editorial Team, "5-Number Summary Calculator — Box Plot Statistics," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/5-number-summary-calculator
@misc{wecalculate_5_number_summary_calculator, title = {5-Number Summary Calculator — Box Plot Statistics}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/5-number-summary-calculator}}, year = {2026}, note = {TG we-Calculate} }
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