Box Plot Analysis Calculator
Enter up to 10 data values to calculate the complete five-number summary (min, Q1, median, Q3, max), interquartile range, fences, and detect outliers for box-and-whisker plot analysis.
A box plot (box-and-whisker plot) is a standardized way to display data distribution based on the five-number summary. The box spans from Q1 to Q3 (containing the middle 50% of data), with a line at the median. Whiskers extend to the smallest and largest values within the fences.
Quartile calculation: The data is sorted and split at the median. Q1 is the median of the lower half, Q3 is the median of the upper half. The IQR (Q3 - Q1) measures the spread of the middle 50%. This calculator uses the exclusive method (median excluded from halves for odd n), which is the most common textbook approach.
Outlier detection: Values below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR are flagged as outliers. The 1.5 multiplier is Tukey's standard; values beyond 3 x IQR are considered extreme outliers. Outliers are plotted as individual points beyond the whiskers.