Box Plot Calculator
This box plot calculator turns a list of numbers into a box and whisker plot and the five-number summary that sits behind it: the minimum, first quartile, median, third quartile and maximum. Paste or type your values, separated by commas or spaces, and the calculator sorts them, finds the quartiles, measures the interquartile range, checks for outliers, and draws the plot so you can see the shape of the data at a glance. The box spans the middle 50% of your values from Q1 to Q3, a line inside it marks the median, and the whiskers stretch to the most extreme readings that still fall within the standard 1.5 times IQR fences. Any value beyond those fences is flagged as an outlier rather than being buried inside a whisker. Box plots are a staple of New Zealand school and university statistics because they compare spread and skew across groups quickly and cope well with messy real data. This tool uses the exclusive quartile method, the version taught in most NCEA and first-year courses, and shows every number it derives so you can follow the working. Use it to summarise test marks, rainfall, response times or any single column of measurements.
For 10 values the median is 16, the middle 50% spans 12 to 25 (IQR 13), and whiskers reach 7 and 41 with no outliers beyond the 1.5 x IQR fences.
Quartiles use the exclusive method (the median is left out of each half). Other methods can shift Q1 and Q3 slightly, so check which your course expects.
How it works
The values are sorted, then the median splits them in two. The lower half gives the first quartile and the upper half gives the third quartile, using the exclusive method so an odd middle value is not counted in either half. The interquartile range is Q3 minus Q1 and measures the spread of the central half. Multiplying the IQR by 1.5 and stepping out from each quartile gives the fences; anything past them is an outlier. The whiskers then reach the smallest and largest values that still sit inside the fences, and the box is drawn from Q1 to Q3 with the median marked inside.
Worked example
Take 7, 8, 12, 13, 14, 18, 21, 25, 30, 41. With ten values the median is the average of the fifth and sixth, (14 + 18) / 2 = 16. The lower half 7, 8, 12, 13, 14 has median 12, so Q1 = 12, and the upper half 18, 21, 25, 30, 41 has median 25, so Q3 = 25. The IQR is 25 - 12 = 13, the fences sit at 12 - 19.5 = -7.5 and 25 + 19.5 = 44.5, and every value is inside them, so the whiskers reach 7 and 41 with no outliers.
Related calculators
- Five-Number Summary Calculator: the summary without the plot.
- Quartile and IQR Calculator: quartiles and spread.
- Median Calculator: the middle value on its own.
- Mean Median Mode Calculator: the common averages.
- Standard Deviation Calculator: spread around the mean.