Box-and-Whisker Plot

History

A box plot is one example of a graphical technique used within exploratory data analysis (EDA). EDA is a statistical method used to explore and understand data from several angles in social science research. EDA grew out of work by John Tukey and his associates in the 1960s and was developed to broadly understand the data, graphically represent data, generate hypotheses and build models to guide research, add robust measures to an analysis, and aid the researcher in finding the most appropriate method for analysis. EDA is especially helpful when the researcher is interested in identifying any unexpected or misleading patterns in the data. Although there are many forms of EDA, researchers must employ the most appropriate form given the specific procedure's purpose and use.

Definition and Construction

One of the first steps in any statistical analysis is to describe the central tendency and the variability of the values for each variable included in the analysis. The researcher seeks to understand the center of the distribution of values for a given variable (central tendency) and how the rest of the values fall in relation to the center (variability). Box plots are used to visually display variable distributions through the display of robust statistics, or statistics that are more resistant to the presence of outliers in the data set. Although there are somewhat different ways to construct box plots depending on the way in which the researcher wants to display outliers, a box plot always provides a visual display of the five-number summary. The median is defined as the value that falls in the middle after the values for the selected variable are ordered from lowest to highest value, and it is represented as a line in the middle of the rectangle within a box plot. As it is the central value, 50% of the data lie above the median and 50% lie below the median. When the distribution contains an odd number of values, the median represents an actual value in the distribution. When the distribution contains an even number of values, the median represents an average of the two middle values.

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