How to
How to make a box plot
A box plot, or box and whisker plot, sums up a set of numbers in five values and shows them in a shape you can compare at a glance. It is the quickest way to put the spread of several groups side by side: which group is higher, which is more consistent, and which has unusual values.
- Enter each group. Type or paste the numbers for one group into its box. Use Add group for more, up to twelve.
- Or paste columns. Copy columns from a spreadsheet, one column per group with the names in the first row, and press Paste from a spreadsheet.
- Read the summary. Under Summary you get the count, minimum, Q1, median, Q3, maximum, IQR, fences, outliers and mean for every group.
- Choose the look. Vertical or horizontal boxes, the mean as a diamond, every value as a dot, and labels for the five numbers.
- Export. Download PNG or SVG, or copy a link that opens the same plot.
How the quartiles are calculated
By default this maker uses the method taught in most US classes and built into TI-83 and TI-84 calculators. Sort the values and find the median. Q1 is the median of the lower half and Q3 is the median of the upper half. When the count is odd, the median itself is left out of both halves. For 1, 3, 5, 7, 9, 11, 13 the median is 7, Q1 is the median of 1, 3, 5, which is 3, and Q3 is 11.
Spreadsheets do it differently. Excel's QUARTILE.INC and Google Sheets' QUARTILE place Q1 at position (n - 1) × 0.25 in the sorted list, counting from 0, and interpolate between neighbors. On the same seven numbers that gives Q1 = 4 and Q3 = 10. Neither is wrong; pick the one your class or report expects with Quartile method.
How outliers are found
The interquartile range is IQR = Q3 - Q1. A value is an outlier if it is more than 1.5 × IQR below Q1 or above Q3. These two limits are the fences. Outliers are drawn as open circles, and each whisker ends at the most extreme value that is still inside the fences, so the whiskers never reach an outlier.
Tip
Turn on Show every data point when a group has fewer than about ten values. The box alone can make a handful of numbers look more certain than they are.
Box plot, histogram or dot plot?
A box plot is best for comparing groups. For the full shape of one group, including two peaks or a gap, use a histogram; for a small set of whole numbers, a dot plot shows every single value. To see how two measurements relate to each other, use a scatter plot.
Questions people ask
What 5 numbers do you need to make a boxplot?
The five-number summary: the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. The box runs from Q1 to Q3 with a line at the median, and the whiskers reach out toward the minimum and maximum. When a value is an outlier, the whisker stops at the most extreme value that is not one, and the outlier is drawn as a separate dot.
How to find 75% of a box plot?
Read the third quartile, Q3: the right edge of the box, or the top edge when the plot is vertical. About 75% of the values are at or below it. In the same way, about 25% are at or below Q1, and the box itself holds the middle 50%.
When not to use a box plot?
When you have only a few values, since five numbers summarize five values badly, or when the shape matters. A box plot cannot show two peaks or gaps in the data. For a small or oddly shaped set, a dot plot or a histogram shows more, and you can turn on 'Show every data point' here to see the values behind each box.
Can Excel generate box plots?
Yes, Excel 2016 and later have a Box and Whisker chart under Insert, Insert Statistic Chart. Its quartiles are calculated its own way, so they can differ slightly from a TI-84 or a textbook. If you are checking a result against Excel's QUARTILE.INC function, switch the quartile method here to Excel QUARTILE.INC.