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## What is a Boxplot?

A boxplot, also called a box and whisker plot, is a way to show the spread and centers of a data set. Measures of spread include the interquartile range and the mean of the data set. Measures of center include the mean or average and median (the middle of a data set).

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, Q
_{1}, 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, Q
_{3}, 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
- Q
_{1}: 160 - Median: 200
- Q
_{3}: 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!*

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step solutions, just like this one!

## Note on Outliers:

Data sets can sometimes contain **outliers** that are suspected to be anomalies (perhaps because of data collection errors or just plain old flukes). If outliers are present, the whisker on the appropriate side is drawn to 1.5 * IQR rather than the data minimum or the data maximum. Small circles or unfilled dots are drawn on the chart to indicate where suspected outliers lie. Filled circles are used for known outliers.

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## How to Make a Box and Whiskers Chart

## Excel

Watch this video on How to Make a Box and Whiskers Chart in Excel, or read the steps below:

Excel does not have a box and whiskers “Insert Graph” function, so you have to build one using stacked bar charts. This is a little more time-consuming than inserting a simple graph, but it you will end up with a great looking box and whiskers graph.

**Note:** This is an advanced Excel technique, so if you are new to Excel you may want to watch the video, which has more information and visuals for each step to make a box and whiskers chart in Excel.

## How to Make a Box and Whiskers Chart in Excel: Steps

**Sample problem:** Make a box and whiskers chart in Excel for the following data set: 25, 145, 145, 148, 178, 178, 198, 201, 222, 210, 565, 589, 485, 333, 358, 158, 257.

Step 1: **Type your data into one column **in an Excel worksheet. For this example, type your data into cells A1:A11.

Step 2: **Click an empty cell type “MIN, Q1, MED, Q3 and MAX” **in a single column. In the next column over, type formulas for MIN, Q1, MED and MAX. The formulas are:

- =MIN(A1:A17)
- =QUARTILE(A1:A17,1)
- =MED(A1:A17)
- =QUARTILE(A1:A17,3)
- =MAX(A1:A17)

Step 3: **In the next column over, type your Min** (in this case, 25) into the cell next to the Min you calculated.

Step 4: **Subtract each value in the previous column from the next value.** In other words, subtract the Min from Q1, the Q1 from the Med, the Med from Q3 and Q3 from the Max.

Step 5: **Highlight the column of differences you calculated in Step 4,** then click “Insert,” then click “Bar” and then click “Stacked Bar.”

## Steps 6 – 10

Step 6: **Click the graph and then click the “Switch Row/Column” button**.

Step 7: **Select the left-hand blue box, right-click and then click “Format Data Series.”**

Step 8: **Click “Fill,” then click the “No Fill” radio button **and then click “Close.”

Step 9: **Add the whisker to the left-hand side **using the following method:

- Click the left-hand red box.
- Select the “Layout” tab, then click “Error Bars”. Next, click “More Error Bar Options.”
- Click “Error Bars with Standard Error.”
- Select the “Layout” tab again, then click “Error Bars” and then click “More Error Bar Options.”
- Click “Mins” and then type the difference between Q1 and the Min into the “Fixed Value” box. For this sample problem, that value is 133.
- Click “Close.”
- Remove the red color (fill) using the technique outlined in Steps 7 and 8 above.

Step 10: **Add the whisker to the right-hand side of the box and whiskers chart Excel **using the following method:

- Click the purple box.
- Select the “Layout” tab, then click “Error Bars” → “More Error Bar Options.”
- Click “Error Bars with Standard Error.”
- Select the “Layout” tab again, then click “Error Bars” → “More Error Bar Options.”
- Click “Plus” and then type the difference between Q3 and the Max into the “Fixed Value” box. For this sample problem, that value is 256.
- Click “Close.”
- Remove the light-blue color (fill) using the technique outlined in Steps 7 and 8 above.

*That’s it: You’ve created a box and whiskers chart in Excel!*

Step 11: (Optional) **Delete the “Series” information from the right:** Click the name and then press the “Delete” key.

**Tip:** If you don’t see an error bar show up, that’s likely because you need to change the line color to “Black” from the More Error Bar Options window.

Check out our YouTube channel for more Excel help and tips!

## TI 83 box plot: Overview

Let’s say you have a list of IQ scores for a gifted classroom in a particular elementary school. The IQ scores are: 118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, 154. That list doesn’t tell you much about anything. However, with a **TI 83 box plot**, the data can come to life.

## Steps

You may find this article helpful if you’ve never entered a list into the calculator before: Entering lists on a TI 83.

**Step 1:** Press STAT, then ENTER, to edit list L1.

**Step 2:** Enter the data from the problem into the list (one value on each line, don’t enter the commas):

118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, 154.

**Step 3:** Press 2nd Y=, to access the **Stat Plot** menu.

**Step 4:** Press ENTER ENTER to turn on **Plot1**.

**Step 5:** Arrow down to **Type**, which has 6 icons to the right of it. Highlight the bottom middle icon, which looks like a syringe with two plungers, and press ENTER to select it.

**Step 6:** Make sure the **XList** entry reads “L_{1}“. If it doesn’t, arrow down to it, Press Clear 2nd 1.

**Step 7:** Press Graph. You should see your Box plot.

**Tip**: If when you press Graph, you see the message “Err: Stat”, or you just don’t see a box plot like you expect to, then press Window, and try different settings. Especially try changing the **Xscl** (X Scale) item to a larger value.

If you prefer an online interactive environment to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

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