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Enter a list of numbers and Axiom draws the box plot with its five-number summary.
Enter up to 1000 numbers separated by commas, spaces, or new lines and press Draw box plot. Read the five-number summary, interquartile range (IQR), and range alongside the plot; the calculator sorts your values automatically.
The five-number summary is minimum, lower quartile Q1, median, upper quartile Q3, and maximum. Quartiles use the median-of-halves method: when the count is odd, leave the overall median out of both halves. The box extends from Q1 to Q3, its line marks the median, and whiskers reach the minimum and maximum. IQR = Q3 − Q1; range = maximum − minimum.
Enter 2, 5, 5, 8. Median = (5 + 5)/2 = 5; Q1 = (2 + 5)/2 = 3.5; Q3 = (5 + 8)/2 = 6.5. The summary is 2, 3.5, 5, 6.5, 8; IQR = 3 and range = 6.
Enter 1, 2, 3, 4, 9. Median = 3; lower half 1, 2 gives Q1 = 1.5; upper half 4, 9 gives Q3 = 6.5. IQR = 5, and range = 9 − 1 = 8.
Quartile conventions differ, especially for small datasets. This tool uses medians of halves and excludes an odd-count median; an interpolated percentile method can give different Q1 and Q3 values.
No. Whiskers reach the actual minimum and maximum. This is not a modified box plot with 1.5 × IQR fences or separately marked outliers.
Yes. Repeated values stay in the data. With a single value, every summary value is that number and both range and IQR are zero; there is no meaningful spread to draw.
No. Width represents the IQR, a measure of spread in the middle part of the ordered data. The plot shows the median, not the mean; use Statistics for the mean and mode.
Use Statistics to add the mean and mode to this visual summary, or Probability for chance calculations. The statistics lesson explains median, quartiles, and why different spread measures tell different stories. Related tools: Statistics Calculator, Probability Calculator. Read the Statistics lesson or practice statistics to build confidence without relying on a calculator.