Box Plot Maker

How to Use the Box Plot Maker

1. 1. Enter the groups. Put one group in each column with the names in the first row — paste straight from a spreadsheet — or switch to One group per line and type Morning: 72, 75, 78. Groups can have different numbers of values.
2. 2. Pick the quartile method. The default takes the median of each half of the data, as the TI-83/84 and most introductory textbooks do. Choose Inclusive to match Excel's QUARTILE.INC, R or NumPy, or Exclusive for QUARTILE.EXC, SPSS and Minitab.
3. 3. Read the plot and the table. Each box runs from Q1 to Q3 with a line at the median; the whiskers reach the most extreme values inside the fences; anything beyond is an outlier. The five-number summary table lists every number the plot is drawn from.
4. 4. Style and export. Choose horizontal or vertical boxes, sort the groups by median, mark the means, add titles and APA style, and download the SVG or PNG.

How a Box Plot Is Built

• The box spans the first quartile (Q1) to the third quartile (Q3), so it holds the middle half of the data. Its length is the interquartile range, IQR = Q3 − Q1.
• The line inside the box is the median.
• The fences sit 1.5 × IQR beyond the box: lower fence = Q1 − 1.5 × IQR, upper fence = Q3 + 1.5 × IQR. They are not drawn — they decide what counts as an outlier.
• The whiskers run from the box to the most extreme data values that are still inside the fences.
• Outliers, the values beyond a fence, are drawn one by one as open circles. This is Tukey's convention from Exploratory Data Analysis (1977). Some software instead runs the whiskers to the minimum and maximum and marks no outliers, so a figure should say which it uses.

Worked Example: The Evening Section

The evening quiz scores in the example, in order, are 58, 59, 61, 62, 63, 64, 66, 68, 70 and 95. There are ten, so the median is the mean of the 5th and 6th values: (63 + 64) ÷ 2 = 63.5. With the median-of-each-half method, Q1 is the median of the lower five values, 61, and Q3 the median of the upper five, 68. So IQR = 68 − 61 = 7, and the fences are 61 − 10.5 = 50.5 and 68 + 10.5 = 78.5. The score of 95 lies beyond the upper fence, so it is drawn as an outlier and the upper whisker stops at 70, the largest score inside the fence.

The differences look small, but they can decide whether a borderline value is an outlier, which is why the method should match your course, your calculator or your statistics package — and why a figure note should say how the whiskers were drawn.

When to Use a Box Plot

Box plots are built for comparing distributions side by side: test scores by class section, reaction times by condition. Each box shows center, spread and skew in a few strokes, and medians and quartiles are not pulled around by extreme values. They also hide things: a box cannot show two clusters, says nothing about how many values sit behind it, and with fewer than about five values its quartiles rest on almost nothing. For a small sample, show the points with a dot plot; for the shape of one large sample, use a histogram.

Box Plots as APA Figures

• Switch on APA style figure; the title leaves the image and the gridlines go. Type the figure number in bold and the title in italic title case above the image — Copy number and title does the formatting for you.
• Define the parts in the note, because conventions differ: Note. Boxes show the interquartile range with the median; whiskers extend to the most extreme values within 1.5 × IQR; circles are outliers; diamonds are means.
• Give each group's n, in the note or in the axis labels, so readers know how much data each box summarizes.

Frequently Asked Questions

How do you find the outliers for a box plot?

Find Q1, Q3 and the interquartile range, IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier. In the evening example, Q1 = 61 and Q3 = 68, so IQR = 7 and the fences are 50.5 and 78.5; the score of 95 is beyond the upper fence and is plotted as a point.

What is the five-number summary?

The minimum, first quartile (Q1), median, third quartile (Q3) and maximum of a data set. A box plot draws the middle three as the box and its center line; the whiskers end at the most extreme values inside the fences, which are the minimum and maximum unless there are outliers. The table under the plot lists all five, the IQR and the fences for every group.

Why are my quartiles different from Excel or my calculator?

Because there are several ways to compute a quartile when it falls between two data values. The TI-83/84 and most textbooks take the median of each half of the data, Excel's QUARTILE.INC and R interpolate inclusively, and QUARTILE.EXC and SPSS interpolate exclusively. Choose the matching option under Quartile method and the box, the fences and the outliers follow it. To compute quartiles on their own, use the Quartile & IQR Calculator.

How long are the whiskers on a box plot?

In a Tukey box plot, at most 1.5 times the IQR. Each whisker stops at the most extreme data value that is still inside its fence, so it is often shorter than 1.5 × IQR, and values further out are drawn as separate points. A whisker can even have no length, if no value lies between a quartile and its fence.

Should a box plot be horizontal or vertical?

Either is correct. Horizontal boxes leave room for long group names and suit many groups; vertical boxes match the usual layout of a value on the y-axis and read well for a few groups with short names. Choose whichever keeps the labels readable.

What does the diamond in a box plot mean?

Here, the mean. Tick Mark the mean with a diamond to add it. Comparing the mean with the median line shows skew: a mean well above the median suggests a long right tail.