How to Make a Box and Whisker Plot on Desmos

Learning how to make a box and whisker plot on Desmos begins with two expressions. Enter your data as a numeric list, such as L=[4,6,7,8,9,11,12,13,15,28]. On the next expression line, type boxplot(L). Desmos then calculates the quartiles and draws the plot automatically.

That basic command is enough for one data set, but a useful graph often needs a few adjustments. You may want to examine the five-number summary, decide how outliers should be handled, move overlapping plots, or change the visible axis range. Desmos provides controls for each of these tasks without requiring you to calculate and draw every line manually.

The instructions below focus on the Desmos Graphing Calculator workflow, including list and table entry, multiple data sets, formatting, interpretation, and common errors.

Quick Answer

Enter the data as a list:

L=[4,6,7,8,9,11,12,13,15,28]

Add another expression and type:

boxplot(L)

Desmos creates the box plot and calculates its quartiles automatically. Open the box-plot expression options to change its vertical offset, height, color, or outlier setting. If the graph is not visible, use Zoom Fit or adjust the axis bounds in Graph Settings.

How to Make a Box and Whisker Plot on Desmos From a List

A list is the fastest input method when the data set is short or already written in one row. Follow these steps:

1. Open the Desmos Graphing Calculator.
2. Select an empty expression line.
3. Name the list with a letter, followed by an equals sign.
4. Place the numeric observations inside square brackets.
5. Separate each number with a comma.
6. Create a new expression line and apply boxplot() to the list.

For this example, enter:

L=[4,6,7,8,9,11,12,13,15,28]

Then enter:

boxplot(L)

The variable name must match in both expressions. If the list is named L, writing boxplot(A) will not work unless a separate list called A exists.

The observations do not need to be arranged from smallest to largest before entry. Desmos processes the list when it creates the graph. If you want to inspect the ordered values, add:

sort(L)

Editing any number in L updates the Desmos box plot immediately. You do not have to delete the graph or run the command again. This dynamic behavior is useful when checking homework, testing sample values, or demonstrating how one observation changes a distribution.

What Desmos Calculates From the Data

A box and whisker plot summarizes a numeric distribution rather than displaying every observation in its original order. Its main features are based on five values:

• Minimum
• First quartile, or Q1
• Median, also called Q2
• Third quartile, or Q3
• Maximum

The central box runs from Q1 to Q3 and contains the middle 50% of the data under the quartile method being used. The line within that box marks the median. The whiskers extend toward the lower and upper ends of the displayed non-outlier range when outliers are identified separately.

You can ask Desmos for a statistical summary by entering:

stats(L)

For the sample list, Desmos uses the Moore and McCabe quartile convention. The ordered data are:

4, 6, 7, 8, 9, 11, 12, 13, 15, 28

The calculations are:

Measure	Calculation	Result
Minimum	Smallest observation	4
Q1	Median of 4, 6, 7, 8, 9	7
Median	(9 + 11) ÷ 2	10
Q3	Median of 11, 12, 13, 15, 28	13
IQR	13 − 7	6
Maximum	Largest observation	28

The interquartile range, or IQR, measures the width of the middle half:

IQR = Q3 − Q1

IQR = 13 − 7

IQR = 6

Using the common 1.5-IQR rule, the potential-outlier fences are:

Lower fence = 7 − 1.5(6) = −2

Upper fence = 13 + 1.5(6) = 22

Because 28 is above 22, it is a potential outlier. The lower whisker reaches 4, while the upper non-outlier whisker reaches 15.

Why another program may show different quartiles

Not all software follows the same quartile convention. Desmos uses the Moore and McCabe method. For an odd number of observations, the overall median is set aside before Q1 and Q3 are found from the lower and upper halves.

Another calculator may include the overall median in both halves or use interpolated percentiles. Its quartiles can therefore differ without either program necessarily containing a calculation error. Compare the methods before deciding that one result is wrong.

Entering Data Through a Desmos Table

A table is often easier than a typed list when you are copying numbers from an experiment, survey, or worksheet. It places each observation in its own cell and makes missing or incorrect entries easier to spot.

To create a box plot from a table:

• Select Add Item in the expression panel.
• Choose Table.
• Enter the observations down one numeric column, such as x₁.
• Add a new expression.
• Enter:

boxplot(x_1)

Desmos treats the table column as a list. Be sure that the column reference in the command matches the column containing your values.

Zoom Fit can help locate the data after table entry. A graph may have been created successfully but remain outside the current viewport because the displayed x-axis does not cover the data range.

Direct list entry and table entry produce the same kind of statistical display. Choose a list for compact data and a table when cell-by-cell editing is more convenient.

Repositioning and Styling the Plot

A standard box plot may appear too close to an axis, too large, or difficult to see against other expressions. Its display controls let you change the presentation without changing the underlying numbers.

The current default plot uses a vertical offset of one unit and a box height of one unit. The offset controls where the plot sits vertically. The height determines how tall the central box appears.

Open the options or input fields associated with the boxplot() expression. From there, you can:

• Increase or decrease the vertical offset.
• Adjust the box height.
• Select another expression color.
• Control the available outlier option.
• Hide the expression temporarily without deleting it.

Changing the offset does not affect the median, quartiles, or whisker values. It only moves the plot up or down. Likewise, changing the height alters its appearance rather than the statistics.

A taller box can be helpful during a classroom demonstration. A smaller height is usually better when several distributions share one graph. Use enough space to distinguish the plots while keeping their numerical axes aligned.

Comparing Two Groups Without Overlap

Multiple box plots allow direct comparisons of center, spread, and unusual observations. Each group needs its own numeric list and box-plot expression.

Enter these two lists:

A=[4,6,7,8,9,11,12,13,15,28]

B=[7,8,10,12,13,14,16,17,19,20]

Then add:

boxplot(A)

boxplot(B)

Both plots may initially occupy the same vertical position, making them look like a single crowded graph. Open the options for each box-plot expression and assign different vertical offsets. For example:

• Set group A to an offset of 1.
• Set group B to an offset of 3.

Choose a different color for each expression. The colors make it easier to connect a plot with its group, but color alone may not be sufficient for a printed or accessibility-focused version.

Desmos does not automatically turn those offsets into named category rows. Add a Note to explain which color and position represent each group. You can also place labeled points near the plots when visible group names are needed inside the graph area.

For three or more groups, continue using separate lists and evenly spaced offsets. Keep the horizontal scale the same so that the distributions remain comparable.

Handling Outliers Without Erasing Evidence

An outlier is an observation that sits unusually far from the middle portion of a distribution under a chosen rule. It is not automatically a typo, measurement failure, or value that should be removed.

The box-plot options include Exclude Outliers. Enabling it excludes detected outlying observations from the data used for that display. This is more than a cosmetic statement that a point is unimportant, so the option should be used deliberately.

Before excluding anything:

• Preserve the original numeric list.
• Check whether the value was entered correctly.
• Consider how the value was produced.
• Explain the exclusion when presenting the graph.
• Compare the original and adjusted displays where appropriate.

For the sample list, 28 is separated from the remaining upper values and exceeds the calculated upper fence of 22. It may represent a genuine extreme result. Removing it merely because it changes the picture can conceal useful information.

The setting may also explain why an expected endpoint or point appears to be missing. Check the expression options before assuming that Desmos lost part of the data.

Setting a Clear Viewing Window

Desmos draws the plot in the coordinate plane, so the visible result depends on the current viewport. Data near 100 will not appear if the x-axis only runs from −10 to 10.

Open Graph Settings to change:

• Minimum and maximum x-axis values
• Minimum and maximum y-axis values
• Axis labels
• Grid visibility
• Numbered axes

Choose horizontal bounds that cover the entire data range and leave a little space at both ends. Set the y-axis wide enough to include every vertical offset and the full box height.

If a graph disappears after you enter a valid command, do not immediately rewrite the expression. First use Zoom Fit or expand the axis range. The plot may simply be off screen.

A descriptive heading can be added outside the calculator when the graph is inserted into a document. Within Desmos, Notes and labeled points can provide context. Label the numeric axis with the measured variable and unit, such as “Time (minutes)” or “Mass (grams),” rather than using a vague title alone.

Why a Desmos Box Plot May Not Appear

Most failed plots come from the data reference, expression syntax, or viewing window. The following checks can locate the problem quickly.

Problem	Likely cause	What to check
boxplot appears undefined	Spelling or syntax error	Use boxplot(L) with parentheses
No plot is visible	Graph lies outside the viewport	Use Zoom Fit or revise axis bounds
List produces an error	It contains text or an undefined item	Keep the input numeric and define every variable
Table data will not plot	The wrong column name was referenced	Match boxplot(x_1) to the populated column
Several plots look like one	They share a vertical offset	Assign a different offset to each expression
Plot resembles a line	Values have little or no spread	Inspect repeated values and the statistical summary
Quartiles differ from a worksheet	Different quartile methods are being used	Check the required convention
A point seems absent	An outlier option or window hides it	Inspect plot options and axis limits

The function expects a numeric list. Quoted words, category labels, empty calculations, or variables without assigned values can prevent it from evaluating correctly.

Also check brackets and parentheses separately. The list uses square brackets:

L=[4,6,7,8]

The function uses parentheses:

boxplot(L)

This distinction is easy to miss when typing on a small screen.

Using Frequency Data Correctly

A frequency table tells you how often each value occurs. A box plot needs the individual observations or an equivalent expanded numeric list.

Suppose the value 2 occurred three times, 5 occurred twice, and 9 occurred once. The expanded data are:

F=[2,2,2,5,5,9]

You can then enter:

boxplot(F)

Do not enter only [2,5,9], because that gives every distinct value equal weight and changes the distribution. The three observations equal to 2 must be represented three times.

For a small data set, repeating the values is straightforward. With a large frequency table, confirm that the method used to expand it produces a normal one-dimensional numeric list. The count() function can help you check the number of observations:

count(F)

Reading the Finished Display

Once the plot is visible, begin with the median. Its horizontal location shows the central value under the selected quartile convention. Comparing median positions can reveal which group tends to have larger values.

Next, inspect the width of each box. A wider box means the middle 50% covers a larger numeric interval, indicating greater spread in that central portion. A narrow box suggests that the middle observations are more tightly grouped.

Unequal whisker lengths or an off-center median can suggest asymmetry. Separate points may indicate potential outliers. These features deserve investigation, but they do not reveal the cause by themselves.

A Desmos box plot does not normally show the mean or display every observation as a dot. It also cannot reveal all details of a distribution. Two data sets can share a similar five-number summary while having different clusters or gaps. If those details matter, compare the box plot with another suitable display or inspect the original list.

Saving, Sharing, and Exporting the Result

Before saving the graph, give lists and Notes meaningful names so another reader can follow the work. Confirm that all required plots are visible and that their offsets and colors remain distinguishable.

Available saving and sharing features can depend on the current Desmos interface and how the calculator is being used. Use the controls shown in your session to save the graph or generate a shareable version. Do not assume that a specific account step is required unless the interface requests it.

For an assignment or report, you can capture the finished graph as an image or use the available export options. Review the exported result rather than assuming it matches the live screen. Make sure labels remain readable, outliers have not been cropped, and the horizontal scale is still visible.

Frequently Asked Questions

What is the Desmos boxplot command?

The command is boxplot(). Put a numeric list or table-column reference inside the parentheses. For example, define L=[3,5,6,8,12] and then enter boxplot(L). Desmos calculates the required quartiles and draws the display from that list.

Does the data need to be sorted before using boxplot()?

No. You can enter the observations in their original order. Desmos processes them when calculating the plot. If you want to verify their order or inspect the distribution more easily, enter sort(L) on another expression line without changing the original list.

How do I create a box plot from a Desmos table?

Add a table and enter the observations down one numeric column. If the populated column is named x₁, create a new expression containing boxplot(x_1). Verify the column reference if the function reports an error or produces no visible result.

How does Desmos calculate Q1 and Q3?

Desmos applies the Moore and McCabe method. With an odd number of observations, it discards the overall median before finding the medians of the lower and upper halves. Other calculators may apply another convention, so a different quartile result is not automatically incorrect.

How can I separate multiple box plots in Desmos?

Give every data set its own list and boxplot() expression. Open the display options and assign a different vertical offset to each plot, such as 1, 3, and 5. Different colors and clear group labels will make the comparison easier to follow.

What does Exclude Outliers do in Desmos?

It excludes detected outlying observations from the data used for that display. It does not establish that those observations are mistakes. Preserve the original list, investigate each unusual value, and explain any exclusion when using the graph in an analysis or assignment.

Why is my Desmos box plot off screen?

The current viewport may not include the data range or the plot’s vertical offset. Use Zoom Fit, or open Graph Settings and extend the x- and y-axis bounds. Also confirm that the expression references a defined numeric list.

Does a Desmos box plot show the mean?

No. The line inside the box represents the median, not the arithmetic mean. A box plot focuses on quartiles, spread, whiskers, and potential outliers. Use a separate calculation if the assignment also requires the mean.

A Reliable Desmos Workflow

The dependable way to remember how to make a box and whisker plot on Desmos is to work in a fixed order: define a numeric list, enter boxplot() with the correct variable, inspect the results with stats(), and then adjust the display.

Use separate offsets for multiple groups, check the viewport before troubleshooting valid syntax, and preserve the original observations when examining outliers. Those habits produce a graph that is not only visible, but also statistically clear and easy to explain.