# How to make box and whisker plots

• A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.
• Box and whisker plots help you to see the variance of data and can be a very helpful tool.
• This guide to creating and understanding box and whisker plots will provide a step-by-step tutorial along with a free box and whisker plot worksheet.
• Let’s get started by looking at some basketball data!

## How to Make a Box and Whisker Plot

Observe the following data set below that shares a basketball players points scored per game over a seven game span:

Step One: The first step to creating a box and whisker plot is to arrange the values in the data set from least to greatest.

In this example, arrange the points scored per game from least to greatest.

1. Step Two: Identify the upper and lower extremes (the highest and lowest values in the data set).
2. The lower extreme is the smallest value, which is 5 in this example.
3. The upper extreme is the highest value, which is 32 in this example.

Step Four: Identify the upper and lower quartiles.

To find the lower quartile and the upper quartile, start by splitting the data set at the median into lower and upper regions.

The upper quartile is the median of the upper region and the lower quartile is the median of the lower region.

In this example, the upper quartile is 20 and the lower quartile is 10.

Now we have all of the information that we will need to construct our box and whisker plot!

Step Five: Construct the Box and Whisker Plot

To construct a box and whisker plot, start by drawing a number line that fits the data set.

Start by plotting points over the number line at the lower and upper extremes, the median, and the lower and upper quartiles.

Next, construct two vertical lines through the upper and lower quartiles, and then constructing a rectangular box that encloses the median value point.

Then construct a vertical line through the median point that extends to the top and bottom of the rectangle.

This is the box in the box and whisker plot.

Finally, draw horizontal lines that connect the lower quartile to the lower extreme and the upper quartile to the upper extreme to complete the box and whisker plot.

The box and whisker plot is complete!

## Create a box and whisker chart

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A box and whisker chart shows distribution of data into quartiles, highlighting the mean and outliers. The boxes may have lines extending vertically called “whiskers”. These lines indicate variability outside the upper and lower quartiles, and any point outside those lines or whiskers is considered an outlier.

Box and whisker charts are most commonly used in statistical analysis. For example, you could use a box and whisker chart to compare medical trial results or teachers' test scores.

1. Select your data—either a single data series, or multiple data series.

(The data shown in the following illustration is a portion of the data used to create the sample chart shown above.)

2. In Excel, click Insert > Insert Statistic Chart >Box and Whisker as shown in the following illustration.

Important: In Word, Outlook, and PowerPoint, this step works a little differently:

1. On the Insert tab, in the Illustrations group, click Chart.

2. In the Insert Chart dialog box, on the All Charts tab, click Box & Whisker.

Tips:

• Use the Design and Format tabs to customize the look of your chart.
• If you don't see these tabs, click anywhere in the box and whisker chart to add the Chart Tools to the ribbon.
1. Right-click one of the boxes on the chart to select that box and then, on the shortcut menu, click Format Data Series.

2. In the Format Data Series pane, with Series Options selected, make the changes that you want.

 Series option Description Gap width Controls the gap between the categories. Show inner points Displays the data points that lie between the lower whisker line and the upper whisker line. Show outlier points Displays the outlier points that lie either below the lower whisker line or above the upper whisker line. Show mean markers Displays the mean marker of the selected series. Show mean line Displays the line connecting the means of the boxes in the selected series. Quartile Calculation Choose a method for median calculation: Inclusive median    The median is included in the calculation if N (the number of values in the data) is odd. Exclusive median    The median is excluded from the calculation if N (the number of values in the data) is odd.
1. Select your data—either a single data series, or multiple data series.

(The data shown in the following illustration is a portion of the data used to create the sample chart shown above.)

2. On the ribbon, click the Insert tab, and then click (the Statistical chart icon), and select Box and Whisker.

Tips:

• Use the Chart Design and Format tabs to customize the look of your chart.
• If you don't see the Chart Design and Format tabs, click anywhere in the box and whisker chart to add them to the ribbon.
1. Click one of the boxes on the chart to select that box and then in the ribbon click Format.

2. Use the tools in the Format ribbon tab to make the changes that you want.

## How to Make a Box and Whisker Plot – Magoosh Statistics Blog

If you’d like to know how to make a box and whisker plot, you’re in the right place. One of the most common uses of the five-number summary is the graph called a “box plot” or “box and whisker plot.” It’s a great way to get a visual look at the five number summary.

### Basics

To make a box and whisker plot, you’ll need to have the five number summary: minimum, first quartile, median, third quartile, and maximum (these are also known as quartiles). Read more about quartiles, and check out our statistics video lessons for even more statistics topics!

Box and whisker plots can be drawn horizontally or vertically. For illustration purposes, we’ll draw one horizontally. It’s the same steps to draw one vertically—just rotated 90 degrees!

The basic idea is to draw a rectangle (the “box”) to represent the middle 50% of a group of numbers, and then one line (or “whisker”) on either side of the box to represent the top 25% and bottom 25%. Let’s look at an example.

### Example of How to Make a Box and Whisker Plot

So, we begin with our five numbers, which summarize a set of data. Let’s say we’re looking at a set of SAT math scores, with a five number summary of 250, 400, 500, 560, and 720.

That means that the lowest score in this group was 250 and the highest score was 720 (the minimum and maximum). The median, 500, means that half the group scored above 500 and the other half below 500. And the quartiles separate out the lowest and highest 25% of the group—so a quarter of the group scored below 400 and a quarter scored above 560.

(Want to read more about the difference between median, mean, and other “averages”? Here’s a quick rundown on mean, median, and mode.)

### Step by Step Instructions

Start with an axis, or number line, to give a reference point. You can either label the axis fully, or just label each of the five numbers on the axis.

Now make a small vertical line above each of the five numbers. These should float a bit above your axis, and not touch the axis.

Next, draw the “box” with horizontal lines connecting the tops and bottoms of the first and third quartile marks.

Finally, create the “whiskers.” Draw one line from the middle of the third quartile mark to the maximum mark, and another line from the middle of the minimum mark to the first quartile mark.

That’s it! Give your graph a title and make sure that the axis is labeled. You’ve created a box and whisker plot! You can see where each of the five numbers from the five number summary are, and can easily compare two groups side-by-side.

## Box and Whisker Plot Maker | Create a Stunning Box Plot with Displayr

Displayr's box and whisker plot maker has a range of options for you to quickly create your free online box plot.

### Step 1

Get started by inputting your data.

### Step 2

Make your box plot beautiful. You can easily customize fonts, colors, backgrounds and sizes.

### Step 3

Share and show off your charts to the world. You can export with one click.

Box plots, also called box and whisker plots or box and whisker graphs are used to show the median, interquartile range and outliers for numeric data. Best of all, it’s super easy to create your box plot using Displayr’s box and whisker plot maker.

Box and whisker plots are best for showing and focusing on the characteristics of the distribution, and to compare the distributions between different variables or groups in your data set.

The ends of the box represent the upper and lower quartiles so the box spans the interquartile range. The median is shown by a vertical or horizontal line in the box. The whiskers are the two lines outside the box that extend to the highest and lowest values or observations within 1.

5 times the interquartile range of the box. You can also create a box plot without the whiskers with our box plot maker.

## Statistics: Power from Data! Box and whisker plots

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• Example 1 – Box and whisker plots
• Summary

A box and whisker plot (sometimes called a boxplot) is a graph that presents information from a five-number summary.

It does not show a distribution in as much detail as a stem and leaf plot or histogram does, but is especially useful for indicating whether a distribution is skewed and whether there are potential unusual observations (outliers) in the data set.

Box and whisker plots are also very useful when large numbers of observations are involved and when two or more data sets are being compared. (See the section on five-number summaries for more information.)

Box and whisker plots are ideal for comparing distributions because the centre, spread and overall range are immediately apparent.

A box and whisker plot is a way of summarizing a set of data measured on an interval scale. It is often used in explanatory data analysis. This type of graph is used to show the shape of the distribution, its central value, and its variability.

In a box and whisker plot:

• the ends of the box are the upper and lower quartiles, so the box spans the interquartile range
• the median is marked by a vertical line inside the box
• the whiskers are the two lines outside the box that extend to the highest and lowest observations.

## Box Plot (Box and Whiskers): How to Read One & How to Make One in Excel, TI-83, SPSS

The box and whiskers chart shows you how your data is spread out. Five pieces of information (the “five number summary“) are generally included in the chart:

• The minimum (the smallest number in the data set). The minimum is shown at the far left of the chart, at the end of the left “whisker.”
• First quartile, Q1, is the far left of the box (or the far right of the left whisker).
• The median is shown as a line in the center of the box.
• Third quartile, Q3, shown at the far right of the box (at the far left of the right whisker).
• The maximum (the largest number in the data set), shown at the far right of the box.

### How to Read a Box Plot

A boxplot is a way to show a five number summary in a chart. The main part of the chart (the “box”) shows where the middle portion of the data is: the interquartile range.

At the ends of the box, you” find the first quartile (the 25% mark) and the third quartile (the 75% mark).

The far left of the chart (at the end of the left “whisker”) is the minimum (the smallest number in the set) and the far right is the maximum (the largest number in the set). Finally, the median is represented by a vertical bar in the center of the box.

Box plots aren’t used that much in real life. However, they can be a useful tool for getting a quick summary of data.

### How to Read a Box Plot: Steps

Step 1: Find the minimum.
The minimum is the far left hand side of the graph, at the tip of the left whisker. For this graph, the left whisker end is at approximately 0.75.

Step 2: Find Q1, the first quartile.
Q1 is represented by the far left hand side of the box. In this case, about 2.5.

Step 3:  Find the median.
The median is represented by the vertical bar. In this boxplot, it can be found at about 6.5.

Step 4: Find Q3, the third quartile.
Q3 is the far right hand edge of the box, at about 12 in this graph.

Step 5: Find the maximum.
The maximum is the end of the “whiskers”: in this graph, at approximately 16.

### Example 2

You can easily read a boxplot to find the five number summary. For example, the above image shows a box and whiskers chart with the following information:

• Minimum: 20
• Q1: 160
• Median: 200
• Q3: 330
• Maximum: 590

Exception: If your data set has outliers (values that are very high or very low and fall far outside the other values of the data set), the box and whiskers chart may not show the minimum or maximum value. Instead, the ends of the whiskers represent one and a half times the interquartile range (1.5*IQR).

All done. That’s how to read a box plot!

## Quartiles, Boxes, and Whiskers

5-Number SummaryIQRs & Outliers

For many computations in statistics, it is assumed that your data points (that is, the numbers in your list) are clustered around some central value; in other words, it is assumed that there is an “average” of some sort. The “box” in the box-and-whisker plot contains, and thereby highlights, the middle portion of these data points.

To create a box-and-whisker plot, we start by ordering our data (that is, putting the values) in numerical order, if they aren't ordered already. Then we find the median of our data.

The median divides the data into two halves. To divide the data into quarters, we then find the medians of these two halves.

Note: If we have an even number of values, so the first median was the average of the two middle values, then we include the middle values in our sub-median computations.

If we have an odd number of values, so the first median was an actual data point, then we do not include that value in our sub-median computations.

That is, to find the sub-medians, we're only looking at the values that have not yet been used.

So we have three points: the first middle point (the median), and the middle points of the two halves (what I've been calling the “sub-medians”). These three points divide the entire data set into quarters, called “quartiles”.

The top point of each quartile has a name, being a “Q” followed by the number of the quarter. So the top point of the first quarter of the data points is “Q1”, and so forth. Note that Q1 is also the middle number for the first half of the list, Q2 is also the middle number for the whole list, Q3 is the middle number for the second half of the list, and Q4 is the largest value in the list.

Once we have found these three points, Q1, Q2, and Q3, we have all we need in order to draw a simple box-and-whisker plot. Here's an example of how it works.

4.3,  5.1,  3.9,  4.5,  4.4,  4.9,  5.0,  4.7,  4.1,  4.6,  4.4,  4.3,  4.8,  4.4,  4.2,  4.5,  4.4

My first step is to order the set. This gives me:

3.9,  4.1,  4.2,  4.3,  4.3,  4.4,  4.4,  4.4,  4.4,  4.5,  4.5,  4.6,  4.7,  4.8,  4.9,  5.0,  5.1

The first value I need to find from this ordered list is the median of the entire set. Since there are seventeen values in this list, the ninth value is the middle value of the list, and is therefore my median:

3.9,  4.1,  4.2,  4.3,  4.3,  4.4,  4.4,  4.4,  4.4,  4.5,  4.5,  4.6,  4.7,  4.8,  4.9,  5.0,  5.1

3.9,  4.1,  4.2,  4.3,  4.3,  4.4,  4.4,  4.4,  4.4,  4.5,  4.5,  4.6,  4.7,  4.8,  4.9,  5.0,  5.1

The median is Q2 = 4.4

The next two numbers I need are the medians of the two halves. Since I used the “4.4” in the middle of the list, I can't re-use it, so my two remaining data sets are:

3.9,  4.1,  4.2,  4.3,  4.3,  4.4,  4.4,  4.4

…and:

4.5,  4.5,  4.6,  4.7,  4.8,  4.9,  5.0,  5.1

The first half has eight values, so the median is the average of the middle two values:

The median of the second half is:

Q3 = (4.7 + 4.8)/2 = 4.75

To draw my box-and-whisker plot, I'll need to decide on a scale for my measurements. Since the values in my list are written with one decimal place and range from 3.9 to 5.1, I won't use a scale of, say, zero to ten, marked off by ones. Instead, I'll draw a number line from 3.5to5.5, and mark off by tenths.

(You might choose to measure from, say, 3 to 6. Your choice would be as good as mine. The idea here is to be “reasonable”, which allows you some flexibility.)

Now I'll mark off the minimum and maximum values, and Q1, Q2, and Q3:

The “box” part of the plot goes from Q1 to Q3, with a line drawn inside the box to indicate the location of the median, Q2:

And then the “whiskers” are drawn to the endpoints:

By the way, box-and-whisker plots don't have to be drawn horizontally as I did above; they can be vertical, too.

As mentioned at the beginning of this lesson, the “box” contains the middle portion of your data. As you can see in the graph above, the “whiskers” show how large is the “spread” of the data.

If you've got a wide box and long whiskers, then maybe the data doesn't cluster as you'd hoped (or at least assumed). If your box is small and the whiskers are short, then probably your data does indeed cluster.

If your box is small and the whiskers are long, then maybe the data clusters, but you've got some “outliers” that you might need to investigate further — or, as we'll see later, you may want to discard some of your results.

98,  77,  85,  88,  82,  83,  87

My first step is to order the data:

77, 82, 83, 85, 87, 88, 98

Next, I'll find the median. This set has seven values, so the fourth value is the median:

The median splits the remaining data into two sets. The first set is 77, 82, 83. The median of this set is:

The other set is 87, 88, 98. The median of this set is:

## Statistics Calculator: Box Plot

This page allows you to create a box plot from a set of statistical data:

1. Enter your data in the text box. You must enter at least 4 values to build the box plot. Individual values may be entered on separate lines or separated by commas, tabs or spaces. You do not need to specify whether the data is from a population or a sample. You may also copy and paste data from another window such as an open document, spreadsheet pdf file or another web page.
2. Press the “Submit Data” button to create the plot.

To clear the graph and enter a new data set, press “Reset”.

When you submit your data, the server calculates the measures that will be used to plot the diagram. These measures are displayed to the left of the chart.For more details on the dispersion of the data set, you may click on the More dispersion data link located on the left of the plot.

### What is a box plot

a box plot is a diagram that gives a visual representation to the distribution of the data, highlighting where most values lie and those values that greatly differ from the norm, called outliers. The box plot is also referred to as box and whisker plot or box and whisker diagram

### Elements of the box plot

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore the vertical width of the central box represents the inter-quartile deviation.

The horizontal line inside the box is the median.

The vertical lines protruding from the box extend to the minimum and the maximum values of the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Values higher than Q3+1.5xIQR or lower than Q1-1.5xIQR are considered outliers and are plotted above the top whisker or below the bottom whisker.

## Box Plots

### Learning Outcomes

• Display data graphically and interpret graphs: stemplots, histograms, and box plots.
• Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.

Box plots (also called box-and-whisker plots or box-whisker plots) give a good graphical image of the concentration of the data. They also show how far the extreme values are from most of the data.

A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them.

To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks one end of the box and the third quartile marks the other end of the box.

Approximately the middle 50 percent of the data fall inside the box. The “whiskers” extend from the ends of the box to the smallest and largest data values. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both.

The box plot gives a good, quick picture of the data.

### Note

You may encounter box-and-whisker plots that have dots marking outlier values. In those cases, the whiskers are not extending to the minimum and maximum values.

Consider, again, this dataset.

1 1 2 2 4 6 6.8 7.2 8 8.3 9 10 10 11.5

The first quartile is two, the median is seven, and the third quartile is nine. The smallest value is one, and the largest value is 11.5. The following image shows the constructed box plot.

The two whiskers extend from the first quartile to the smallest value and from the third quartile to the largest value. The median is shown with a dashed line.

### Note

It is important to start a box plot with a scaled number line. Otherwise the box plot may not be useful.

• The following data are the heights of 40 students in a statistics class.
• 59 60 61 62 62 63 63 64 64 64 65 65 65 65 65 65 65 65 65 66 66 67 67 68 68 69 70 70 70 70 70 71 71 72 72 73 74 74 75 77
• Construct a box plot with the following properties; the calculator instructions for the minimum and maximum values as well as the quartiles follow the example.
• Minimum value = 59
• Maximum value = 77
• Q1: First quartile = 64.5
• Q2: Second quartile or median= 66
• Q3: Third quartile = 70
1. Each quarter has approximately 25% of the data.
2. The spreads of the four quarters are 64.5 – 59 = 5.5 (first quarter), 66 – 64.5 = 1.5 (second quarter), 70 – 66 = 4 (third quarter), and 77 – 70 = 7 (fourth quarter). So, the second quarter has the smallest spread and the fourth quarter has the largest spread.
3. Range = maximum value – the minimum value = 77 – 59 = 18
4. Interquartile Range: IQR = Q3 – Q1 = 70 – 64.5 = 5.5.
5. The interval 59–65 has more than 25% of the data so it has more data in it than the interval 66 through 70 which has 25% of the data.
6. The middle 50% (middle half) of the data has a range of 5.5 inches.

Solution:

To find the minimum, maximum, and quartiles:

Enter data into the list editor (Pres STAT 1:EDIT). If you need to clear the list, arrow up to the name L1, press CLEAR, and then arrow down.

Put the data values into the list L1.

Press STAT and arrow to CALC. Press 1:1-VarStats. Enter L1.

1. Press ENTER.
2. Use the down and up arrow keys to scroll.
3. Smallest value = 59.
4. Largest value = 77.

Q1: First quartile = 64.5.

• Q2: Second quartile or median = 66.
• Q3: Third quartile = 70.
• To construct the box plot:

Press 4:Plotsoff. Press ENTER.

Arrow down and then use the right arrow key to go to the fifth picture, which is the box plot. Press ENTER.

Arrow down to Xlist: Press 2nd 1 for L1

Arrow down to Freq: Press ALPHA. Press 1.

Press Zoom. Press 9: ZoomStat.

Press TRACE, and use the arrow keys to examine the box plot.

The following data are the number of pages in 40 books on a shelf. Construct a box plot using a graphing calculator, and state the interquartile range.

136 140 178 190 205 215 217 218 232 234 240 255 270 275 290 301 303 315 317 318 326 333 343 349 360 369 377 388 391 392 398 400 402 405 408 422 429 450 475 512

IQR = 158

This video explains what descriptive statistics are needed to create a box and whisker plot.

## How to Make a Box and Whisker Plot

1. 1

Gather your data. Let's say we start the numbers 1, 3, 2, 4, and 5. These will be used for calculation examples.

2. 2

Organize the data from least to greatest. Take all your numbers and line them up in order, so that the smallest numbers are on the left and the largest numbers are on your right. In our case, the order of the numbers is 1, 2, 3, 4, and 5.[1]

3. 3

Find the median of the data set. The median is the middle number in an ordered data set. (This is why we lined up all the numbers in Step 2.) For the data set in our example, 3 is the number that's exactly in the middle, and therefore is our median. The median is also called the second quartile.[2]

• In a data set with an odd amount of numbers, the median will always have the same amount of numbers on either side of it. For the data set 1, 2, 3, 4, 5, the median number, 3, has 2 numbers before it and 2 numbers after it. That's how we can be sure that it's our median.
• What if the data set you're working with has an even amount of numbers? What if you had to find the median of 2, 4, 4, 7, 9, 10, 14, 15? You find the median here by taking the two middle numbers and finding their average. In our example, you would take 7 and 9 — the two middle numbers — add them up and divide them by 2. 7 + 9 equals 16, and 16 divided by 2 equals 8. The median of this data set would be 8.
4. 4

Find the first and third quartiles. We've already found the second quartile of the data set, which is our median.

Now we need to find the median of the lower half of the data set; in our example it would be the median of the two numbers to the left of 3. The median of 1 and 2 is (1 + 2) / 2 = 1.5.

Do the same to find the median of the two numbers to the right of 3. (4 + 5) / 2 = 4.5.[3]

5. 5

Draw a plot line. This should be long enough to contain all of your data, plus a little extra on either side. Make sure to place the numbers at even intervals. If you're dealing with decimals, such as 4.5 and 1.5, be sure to label them as well.

6. 6

Mark your first, second, and third quartiles on the plot line. Take the values of your first, second, and third quartiles and make a mark at those numbers on the plot line. The mark should be a vertical line at each quartile, starting slightly above the plot line.[4]

7. 7

Make a box by drawing horizontal lines connecting the quartiles. Connect the top or the first quartile to the top of the third quartile, going through the second quartile. Connect the bottom of the first quartile to the bottom of the third quartile, making sure to go through the second quartile.[5]

8. 8

Mark your outliers. Find the smallest, and then the largest, numbers in your data set and mark them on the plot line. Mark these points with a small dot. In the case of our example, the lower outlier is 1 and the upper outlier is 5.[6]

9. 9

Connect your outliers to the box with a horizontal line. The straight line that connects the outliers is informally called the “whiskers” of the box and whiskers plot.

10. 10

Finished. Look at a box and whiskers plot to visualize the distribution of numbers in any data set. You can easily see, for example, whether the numbers in the data set bunch more in the upper quartile by looking at the size of the upper box, as well as the size of the upper whisker. Box and whisker plots are great alternatives to bar graphs and histograms.[7]