How to use
A box plot summarizes the location and spread of a numerical sample. Use this calculator to check a classroom exercise, inspect a small set of measurements, or report a five-number summary with the convention stated. Enter individual observations, including repetitions. This page handles one sample at a time; it does not compare groups or estimate a population distribution.
- Replace the example values with your own data. Use a decimal point, even when your language normally uses a decimal comma.
- Choose Calculate or press Enter. Read the result together with the plot and the detailed table.
- Copy result copies the confirmed numbers as plain text. Editing an input clears the previous result and copy state, while the graph previews valid current inputs. Clear empties inputs, results and graph without restoring the example.
How it works
The calculator sorts the observations and uses the median-of-halves method, excluding the overall median when the sample size is odd. For an even number of observations, each half contains exactly half the data. The median of the lower half is Q1 and the median of the upper half is Q3. For a single observation, all three quartiles equal that value. This convention is explicit because percentile interpolation and inclusive-median methods can give different answers.
The interquartile range is IQR = Q3 − Q1. Detection fences are Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Values strictly beyond them are flagged as outliers; values exactly on a fence remain inside. Whiskers end at actual observations within the fences, not at the theoretical fence numbers. The data minimum and maximum still include outliers. The box, median line, whiskers and circles all use these same calculated values.
Examples
Even sample: 1, 2, 3, 4 gives minimum 1, Q1 = 1.5, median 2.5, Q3 = 3.5 and maximum 4. IQR = 2, with fences −1.5 and 6.5. No value is outside, so the whiskers end at 1 and 4.
Odd sample with an outlier: 1, 2, 3, 4, 5, 6, 7, 8, 30 gives median 5, Q1 = 2.5 and Q3 = 7.5. IQR = 5, with fences −5 and 15. The upper whisker is 8 although the maximum is 30. The point at 30 is flagged.
Uses and limits
Supply 1–200 numbers separated by spaces, commas or semicolons. A comma separates observations: 1,5 means two values, not one decimal. Use 1.5 for a decimal and omit thousands separators. Zero is accepted; nonzero magnitudes must be between 10⁻⁹ and 10⁹, with at most 15 significant digits. Text labels, missing-value markers and units are rejected rather than silently discarded.
A box plot is useful for spotting spread and possible unusual observations, but it hides detailed clusters and repeated values. An outlier flag is a prompt to inspect the source, not proof of a measurement error or permission to delete it. Very small samples offer little evidence about the wider population. Numeric display is rounded for readability; exact input distinctions are retained internally.
Frequently asked questions
Why does another calculator give different quartiles?
Check its quartile definition first. Inclusive halves or interpolated percentiles can disagree with this median-of-halves rule, especially for small odd samples. Report the method alongside the result.
Are the whiskers the minimum and maximum?
Only when those extreme observations fall inside the fences. An outlier can extend beyond a whisker; the result lists both kinds of endpoints separately.
What if every value is the same?
The IQR is zero and the box collapses to a line. Every observation lies on the same boundary, so none is flagged. A single observation follows the same display convention.
Can I save the plot?
Copy result provides the numerical summary and landmarks as text. This page has no image export or persistent dataset storage. Keep your original data and the stated quartile method with your report.