Five-Number Summary & Box Plot Calculator
Turn a data set into its box-plot five-number summary — min, Q1, median, Q3, max — plus range, IQR, whisker fences and flagged outliers.
How it works
IQR = Q3 − Q1 · Whiskers reach to the last point inside Q1 − 1.5·IQR and Q3 + 1.5·IQR
A box plot draws exactly five numbers: the minimum, first quartile, median, third quartile and maximum. The box spans Q1 to Q3 — the middle half of the data — and the line inside marks the median. Whiskers stretch out to the furthest points still within 1.5 IQR of the box, and anything past those fences is drawn as an individual outlier point.
Worked example
For 4, 8, 15, 16, 23, 42, 4, 11, 19, the sorted data is 4, 4, 8, 11, 15, 16, 19, 23, 42 (median 15). The lower half gives Q1 = 6 and the upper half Q3 = 21, so IQR = 15 and the upper fence is 21 + 22.5 = 43.5 — no point exceeds it, so 42 is the top whisker, not an outlier.
Sources: Five-number summary — Wikipedia
Frequently asked questions
How are Q1 and Q3 defined here?
The data is split at the median into a lower and upper half; Q1 is the median of the lower half and Q3 the median of the upper half. With an odd count the overall median is left out of both halves, following Tukey’s method used for box plots.
What is the difference between the range and the IQR?
The range is maximum minus minimum and reflects the full spread, so a single extreme point can dominate it. The IQR covers only the middle 50% of the data, which makes it far more resistant to outliers.
Why does a box plot mark outliers separately?
Drawing points beyond the 1.5 IQR fences as dots keeps the whiskers representative of the bulk of the data while still showing extreme values, so you can spot them without letting them distort the box.
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For education — check the assumptions (sample size, independence, distribution) before using these statistics in real decisions.