Unit 55: Box Plots

Box plots, or box-and-whiskers, are one of the data representations that show up on the SAT.  They are used to show information about a set of data and divide it into quarters.

They can appear horizontal:

or vertical, or with several plots on the same figure.

So how do they work?  First, the box part. 

The ends of the box represent the 25th and 75th percentile of the data.  So contained within the box is the middle 50% of data.  In our example here, if there were 100 data points in this set, 25 of them would be less than 25 minutes, and 25 would be more than 40 minutes.  50 data points would be contained in the box.  We don’t know, or frankly care, what those individual data points are.

Next, the line inside of the box.  This represents the median of the data set (half the values above, and half the values below).  Note that depending on the data set, this might fall in the middle of the box, or it might not.  In our example, the median is at 35.

Finally, the whiskers.

These show the minimum and maximum values, and along with this the first and last quartiles (a quartile is one quarter of the data).  So in this data set:

  • the lowest value was 15, 
  • one quarter of the values were between 15 and 25, 
  • half the values were between 25 and 40, 
  • one quarter of the values were between 40 and 60,
  • the median was 35,  
  • the range of this data set is 45 (from 15 to 60).

Strategy:

  1. The box shows the middle 50th percentile of the data, from the 25th to 75th percentiles.
  2. The line in the box shows the median.
  3. The “whiskers” show the remaining quarters, and end at the minimum and maximum for the data set.
  4. The range of the data set is just the maximum minus the minimum.