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# Boxplot

last edited by 7 years ago

A boxplot (or box plot) is a graphical representation of a 5-Number Summary. It is used as a means of displaying quantitative data in a way that makes it easy to see many of the critical features (Quartiles, skewness, outliers, center, etc...) of a data set. A box plot has a central box bounded by the first and third quartiles containing the middle fifty percent of the data along with median. The central box has two vertical lines extending from both ends, bounded by the minimum and maximum values. Any outliers would be displayed as dots outside the minimum and maximum. An extreme outlier would be represented by a asterisk. An outlier is defined by outlier fences, which occur at Q3+1.5*IQR, and Q3-1.5*IQR Where Q3=Quartile three and IQR=Q3-Q1.

A boxplot is a one of many ways to display the basic shape, distribution, and spread of a data set with one quantitative variable. Quantitative data is anything measured on a numerical scale such as the number of animals one may own, how much money is being spent, or how many calories fast food has.

For example, take the marijuana use of 16 year olds in various countries. The data is given in percentages. These percentages represent the number of teens that report to have tried marijuana.  At this point we need to formulate a five number summary. A five number summary is comprised of the minimum value, maximum value, median, first quartile, and third quartile. We use these five numbers to then create the boxplot.

One can see here that the min, 1st quartile, median, 3rd quartile, and maximum values are all displayed. The median value is a little under twenty percent while the maximum is close to forty five. The IQR reports fifty percent of the data gathered and is represented by the box. This box suggests that the middle fifty percent of data gathered will fall between 9% and 26%. This means that the middle fifty percent of countries in this sample report between 9% and 26% of their 16 year olds as having smoked marijuana.

## Generating a boxplot in SPSS:

• When creating a boxplot you must click on the "Graphs" menu on the ribbon and select "Chart builder".
• This will open the chart builder dialog box, in which you will select the boxplot option from the chart gallery.
• Click and drag the "simple boxplot" (the first box in the boxplot options section) to the chart preview section.
• You then will need to drag your quantitative variable to the box adjacent to the y axis.
• Click "Okay"
• A boxplot will be generated and placed within the output section of SPSS.
• To alter the range of the boxplot, you must first double click the boxplot itself to open the chart editor.
• Once the editor is open you must double click the numbers marking the scale on the y axis to bring up the chart options.
• Then, in chart options, click the "scale" tab where you will find options to adjust min, max, and scale.
• Adjust these parameters to the desired values and click apply.
• Close chart options and chart editor.
• The boxplot will appear within the output window with the current alterations.

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