# GRE Data Analysis - Box Plots

On the GRE exam, you may be asked to interpret a data set using one of several graphical representations of the data. One convenient way to describe a data set is to use a box plot (also known as a box-and-whisker diagram or plot). A box plot graphically displays groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q_{1}), median (M), upper quartile (Q_{2}), and largest observation (sample maximum). The **quartiles** of a set of values are the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled. The box plot is often called a "whisker" plot because "whiskers" extend outward from the boxes to the least and greatest values. Graphically, a box plot looks like the following:

Sometimes, the Median is denoted as Q_{2}, and the upper quartile is denoted as Q_{3}. In the above box plot, the median is 4, the sample minimum is 0, the sample maximum is 9, the lower quartile is 2, and the upper quartile is 7.

A measure of the dispersion of the data that is shown in a box plot is called the **interquartile range**, which is the difference between
the upper quartile and the lower quartile. In the above box plot, the interquartile range is 7-2=5.

ExampleGRE Question |
The below box plot is for the following set
- 1
- 4
- 5
- 6
- 9
Solution: If you are familiar with box plots, then the following details are easily calculated:- The lowest data point is 1
- The lower quartile is 4
- The median is 8
- The upper quartile is 10
- The largest observation is 10
- The range is 10-1 = 9
- The interquartile range is 10-4=6
Thus the answer is |