How to Read a Box and Whisker Plot Interquartile Range

Contents (Click to skip to that section):

• What is a Boxplot?
• How to Read a Box Plot
• How to Make a Box Plot:
  • Excel
  • TI-83
  • TI-89
  • SPSS
  • Minitab

What is a Boxplot?

Watch the video for an overview and how to make one by hand:

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The box and whiskers chart shows y'all how your information is spread out. Five pieces of information (the "v number summary") are generally included in the nautical chart:

• The minimum (the smallest number in the information ready). The minimum is shown at the far left of the chart, at the end of the left "whisker."
• Outset quartile, Q₁, is the far left of the box (or the far correct 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 fix), shown at the far correct of the box.

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How to Read a Box Plot

A boxplot is a manner to show a five number summary in a chart. The master part of the chart (the "box") shows where the middle portion of the information is: the interquartile range. At the ends of the box, y'all" find the starting time 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 prepare) and the far right is the maximum (the largest number in the fix). Finally, the median is represented by a vertical bar in the center of the box.

Box plots aren't used that much in existent life. Still, they tin be a useful tool for getting a quick summary of data.

How to Read a Box Plot: Steps

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

Footstep 2: Find Q1, the kickoff quartile.
Q1 is represented by the far left hand side of the box. In this example, about 2.5.

Footstep 3: Detect the median.
The median is represented by the vertical bar. In this boxplot, it tin can be found at about 6.v.

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

Step five: Find the maximum.
The maximum is the finish of the "whiskers": in this graph, at approximately xvi.

Example 2

You can easily read a boxplot to observe the five number summary. For instance, the above epitome shows a box and whiskers nautical chart with the following information:

• Minimum: 20
• Q₁: 160
• Median: 200
• Q_three: 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 up), the box and whiskers nautical chart may not show the minimum or maximum value. Instead, the ends of the whiskers stand for one and a half times the interquartile range (1.5*IQR).

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

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Note on Outliers:

Data sets tin can sometimes incorporate outliers that are suspected to be anomalies (maybe because of data collection errors or merely apparently former flukes). If outliers are nowadays, the whisker on the advisable side is drawn to one.5 * IQR rather than the information 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 Nautical chart

Excel

Watch this video on How to Brand a Box and Whiskers Chart in Excel.

Can't see the video? Click here.

Excel does not have a box and whiskers "Insert Graph" function, and then you have to build one using stacked bar charts. This is a little more than time-consuming than inserting a simple graph, merely it yous will finish up with a great looking box and whiskers graph.

Note: This is an advanced Excel technique, and then if you are new to Excel y'all may want to spotter the video, which has more information and visuals for each stride to make a box and whiskers nautical chart in Excel.

How to Make a Box and Whiskers Nautical chart in Excel: Steps

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

Step 1: Blazon your data into one column in an Excel worksheet. For this instance, blazon your data into cells A1:A11.

Pace 2: Click an empty cell type "MIN, Q1, MED, Q3 and MAX" in a single column. In the adjacent column over, type formulas for MIN, Q1, MED and MAX. The formulas are:

• =MIN(A1:A17)
• =QUARTILE(A1:A17,one)
• =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 adjacent to the Min you calculated.

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

Step five: Highlight the cavalcade of differences you calculated in Pace 4, then click "Insert," so click "Bar" and so click "Stacked Bar."

Steps vi – x

Step 6: Click the graph and and so click the "Switch Row/Column" button.

Stride 7: Select the left-manus blue box, right-click and then click "Format Information Series."

Step 8: Click "Fill," then click the "No Fill" radio button so click "Shut."

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

1. Click the left-mitt red box.
2. Select the "Layout" tab, then click "Error Confined". Side by side, click "More Mistake Bar Options."
3. Click "Fault Confined with Standard Error."
4. Select the "Layout" tab again, and so click "Error Confined" then click "More Fault Bar Options."
5. Click "Mins" and then blazon the difference between Q1 and the Min into the "Fixed Value" box. For this sample problem, that value is 133.
6. Click "Close."
7. Remove the carmine color (fill up) using the technique outlined in Steps seven and 8 to a higher place.

Pace x: Add the whisker to the correct-hand side of the box and whiskers chart Excel using the following method:

1. Click the purple box.
2. Select the "Layout" tab, then click "Error Bars" → "More than Error Bar Options."
3. Click "Error Bars with Standard Fault."
4. Select the "Layout" tab once more, then click "Error Bars" → "More than Error Bar Options."
5. Click "Plus" and then blazon the difference between Q3 and the Max into the "Fixed Value" box. For this sample problem, that value is 256.
6. Click "Close."
7. Remove the calorie-free-bluish color (fill) using the technique outlined in Steps seven and 8 above.

That's it: Yous've created a box and whiskers nautical chart in Excel!

Step 11: (Optional) Delete the "Series" information from the correct: Click the name and so press the "Delete" key.

Tip: If you don't see an error bar prove upwardly, that's probable because y'all need to alter the line color to "Blackness" from the More Mistake Bar Options window.

Bank check out our YouTube channel for more than Excel assist and tips!

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TI 83 box plot: Overview

Permit'southward say you have a listing 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 listing doesn't tell you lot much nigh 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 listing into the calculator before: Inbound lists on a TI 83.

Step ane: Press STAT, so ENTER, to edit list L1.

Step 2: Enter the information from the trouble into the listing (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.

Stride 3: Press second Y=, to access the Stat Plot card.

Step iv: Press ENTER ENTER to plough on Plot1.

Step 5: Arrow down to Blazon, which has 6 icons to the right of it. Highlight the bottom center icon, which looks like a syringe with 2 plungers, and press ENTER to select it.

Stride 6: Make certain the XList entry reads "L₁". If it doesn't, arrow down to it, Press Clear 2nd 1.

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

Tip: If when you press Graph, you see the message "Err: Stat", or you just don't come across a box plot like you expect to, then press Window, and try dissimilar settings. Particularly try changing the Xscl (X Scale) particular to a larger value.

TI-89

Example problem: Create a box and whiskers chart with the following data: 100, 340, 400, 350, and 400.

Footstep 1: Create a new folder chosen "Box." From the Home screen, press F4 and curl down to NewFold (option B). Press ENTER.

Step 2: Press 2nd Alpha ( – x to spell B O X and printing ENTER.

Stride three: Press APPS, then curl downward to Stats/Listing Editor. Press ENTER twice.

Step 4: Printing the downward arrow fundamental to get to the first line of the list. Enter your data into list1. Follow each entry with a comma: 100, 340, 400, 350, 400.

Step 5: Press F2 and then 1 to enter Plot Setup.

Stride 6: Press F1, right arrow, and 5 to select mod box plot.

Step seven: Arrow down to Mark and select box.

Pace 8: Arrow down and enter B O 10 (using the alphanumeric keypad) in the x. Press ENTER.

That'southward information technology!
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SPSS

SPSS allows you to create two types of boxplots: simple and amassed. Which type of boxplot you choose depends upon how many variables yous desire to plot. Cull the unproblematic chart option when yous desire to create a plot of one variable, and cull the clustered boxplot choice if you want to create a comparison of variable types. SPSS boxplots can be created in the Nautical chart Architect or in the Legacy Dialogs menu.

Box plot in SPSS: Steps

Scout the video to run across how to make a boxplot in SPSS using the Nautical chart Builder, or read the steps beneath for a slightly dissimilar mode to make a boxplot in SPSS, by using the legacy dialog.

Can't see the video? Click here.

Step 1: Open an existing worksheet with your data or blazon your data into a new worksheet.

Step two: Click "Graphs," then click "Legacy Dialogs" and and so click "Boxplot."

Step three: Click the type of nautical chart you desire to brandish, either Simple or Clustered, then click a radio button for either summaries of groups or split variables.

Stride iv: Click "Define" to open up the "Define Simple Boxplot" dialog box.

Stride 5: Click a variable in the left window that y'all want to see medians or IQRs for. This is the belittling variable, the 1 that will be displayed on the y-centrality. Click the height pointer to move the variable to the "Variable" window.

Step half dozen: Click a second variable in the left window that you desire to display on the x-axis (the categorical variable), and then click the 2d pointer down, to the left of Category Axis.

Step 7: Click "OK" to display the boxplot.

Minitab Box Plot

Thanks to Minitab's like shooting fish in a barrel-to-use graph creation software, you tin can make a box plot in Minitab in a couple of clicks. Lookout man this video on how to make a box plot in Minitab:

Tin can't run into the video? Click hither.

Step 1: Type your data into columns in a Minitab worksheet. Typically, yous'll want to blazon in 2 columns of data, one categorical and i quantitative (numerical).

Step ii: Click "Graph" on the toolbar then click "Boxplot."

Footstep three: Choose a type of boxplot. If your information is in the form of column of quantitative data and one cavalcade of chiselled variables (the near mutual scenario) so choose "Ane y" "With groups".

Step four: Click a variable proper name for your quantitative/numerical information and and then click "Select" to move the item to the Graph Variables box.

Step five: Click a variable name for your categorical data so click "Select" to move that item to the Categorical Variables box.

Step iv: Click "OK" to create a boxplot.

That'southward information technology!

Tips: Mouse over ane of the boxes to display a window showing the median, Q1, Q3 and the IQR. You lot can as well click on a number to bring up the Edit Calibration box to specify labels, scales and other attributes for the boxplot.

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References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Wheelan, C. (2014). Naked Statistics. West. West. Norton & Company
Salkind, Northward. (2016). Statistics for People Who (Think They) Hate Statistics: Using Microsoft Excel quaternary Edition.

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