Box Plot Calculator — Five-Number Summary & IQR
Enter a list of numbers to get the complete five-number summary — minimum, Q1, median, Q3, maximum — plus the IQR, Tukey outlier fences and a box-plot number line showing the spread.
Q3 − Q1 — the spread of the middle 50% of data
- 1
Q1 — median of lower half
10Median of all values below the dataset median (exclusive method). - 2
Q3 — median of upper half
25 - 3
IQR = Q3 − Q1
25 − 10 = 15
How does this calculator work?
A box plot summarises data with five numbers: min, Q1 (25th percentile), median (50th), Q3 (75th), and max. IQR = Q3 − Q1 covers the middle 50% of data. Values outside Q1 − 1.5·IQR or Q3 + 1.5·IQR are potential outliers. Enter at least four numbers to compute the full summary.
Formula
How this is calculated
The calculator sorts the values and applies the exclusive (textbook) method for quartiles. The median Q2 is the middle value for an odd count or the average of the two middle values for an even count. Q1 is the median of all values below Q2 and Q3 is the median of all values above Q2 (the median itself is excluded from both halves).
The interquartile range IQR = Q3 − Q1 measures the spread of the central 50% of the data, making it resistant to extreme values. The Tukey fences (Q1 − 1.5·IQR and Q3 + 1.5·IQR) are the most widely taught outlier boundaries: any value beyond a fence is flagged as a potential outlier. The whiskers of a standard box-and-whisker plot extend to the most extreme non-outlier values inside those fences.
At least four data points are required to produce meaningful quartiles. The quartile method used here (sometimes called Method 1 or the exclusive method) is the one taught in most secondary-school and introductory statistics courses; alternative methods (e.g. inclusive quartiles or the method used by some statistical software) may give slightly different Q1/Q3 values for small datasets.
Frequently asked questions
The IQR is the distance between the 25th and 75th percentiles — the range of the middle half of the data. A larger IQR means more spread in the central portion of the dataset; it is less affected by outliers than the full range.
Values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR are flagged as potential outliers using Tukey's fence rule. This is a widely used heuristic; outliers identified this way warrant investigation but are not automatically invalid data points.
There are several quartile conventions. This calculator uses the exclusive method (median excluded from both halves), common in secondary school. Statistical software such as R or Excel may use different interpolation rules, giving slightly different Q1 and Q3 for some datasets.
Also known as
TG we-Calculate Editorial Team. (2026). Box Plot Calculator — Five-Number Summary & IQR [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/box-plot-calculator
TG we-Calculate Editorial Team. "Box Plot Calculator — Five-Number Summary & IQR." TG we-Calculate. 2026. https://we-calculate.com/calculator/box-plot-calculator.
TG we-Calculate Editorial Team, "Box Plot Calculator — Five-Number Summary & IQR," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/box-plot-calculator
@misc{wecalculate_box_plot_calculator, title = {Box Plot Calculator — Five-Number Summary & IQR}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/box-plot-calculator}}, year = {2026}, note = {TG we-Calculate} }
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