What a box plot shows
A box plot turns a column of numbers into a picture of where the values sit and how far they spread. The box spans the first quartile to the third quartile, so it holds the middle half of the data. The line across the box is the median. The whiskers reach the furthest value that is still within 1.5 interquartile ranges of the box, so a whisker always ends on a real observation rather than on the fence itself. Any value beyond a fence is drawn as its own point. The form and the 1.5 convention come from Tukey's Exploratory Data Analysis [Tukey 1977].
An outlier is a value worth looking at, not a value to delete. The 1.5 rule is a convention for drawing attention, not a test. In a large sample, some points will fall outside the fence in perfectly ordinary data.
The three data shapes this tool accepts
You can paste your numbers in any of these layouts:
- A column of group names next to a column of values, with one row per observation. This is the usual shape of raw data.
- One numeric column per group. Each column becomes one box.
- A single column of numbers for one box.
The tool charts at most 30 groups and says so when there are more. The five-number summary for every group is printed under the chart, with any outliers listed.
Worked example
Suppose you paste two columns. The first column holds group names: A, A, A, A, A, B, B, B, B, B. The second column holds values: 2, 4, 4, 4, 5, 1, 3, 3, 3, 9. For group A, the median is 4, the first quartile is 4 and the third quartile is 4. The interquartile range is 0, so the whiskers reach the furthest values within 1.5 times 0 of the box, which is 0. Every value sits on the box, and no point is drawn outside it. For group B, the median is 3, the first quartile is 3 and the third quartile is 3. The interquartile range is 0 again, so the value 9 is drawn as its own point. The five-number summary under the chart lists both groups, and the outlier for B is named.
When a box plot is the right choice
A box plot is for comparing several groups at once on one axis. A histogram per group would take too much room, and a bar chart of means would hide the spread. If you have five groups and want to see which one sits higher and which one spreads wider, a box plot does that in one picture.
It is the wrong choice when you need to see the shape of a single distribution. A box plot shows position and spread but hides shape. A distribution with two separate humps and a flat one can produce the same box. Pair it with a histogram before concluding anything about shape.
Quartiles and how they are defined here
Quartiles on this site use linear interpolation between order statistics. This is R's default type 7 and the definition Excel's PERCENTILE function uses, so a reader checking against their spreadsheet gets the same answer [Hyndman & Fan 1996]. Tukey's original hinges and Excel's exclusive method can give a slightly different box on small samples. The full references are on the how it works page.
The tool reads your pasted text by finding the delimiter itself. A tab wins if any line contains one, otherwise a comma, semicolon or pipe, whichever splits the lines most consistently. A single column of numbers needs no delimiter. Quoted fields follow the ordinary CSV convention [RFC 4180]. A first row is treated as headings only when the rows below it are numbers or dates and the first row is not. Rows with fewer columns than the widest row are padded and the count is reported, never dropped.
Numbers are read column by column. The decimal separator is decided once per column from all of its values, because "1,234" is one thousand two hundred and thirty-four in a US sheet and 1.234 in a German one. Currency symbols, trailing units and spaces are ignored. A value in parentheses is negative. Empty cells and spreadsheet placeholders such as n/a or #DIV/0! are counted as empty rather than treated as zero.
You get a PNG drawn at twice the chart's size, and an SVG that stays sharp at any size. There is no watermark, no sign-up and no limit on the number of charts. The chart carries a title and a description in the file itself so a screen reader can announce it, and the figures behind every chart are also shown as a table on the page [WCAG 2.2, success criterion 1.1.1].