Percentiles and Box PlotsPercentiles  We saw that the median splits the data so that half lies below the median.  Often we are interested in the percent of the data that lies below an observed value.   We call the rth percentile the value such that r percent of the data fall at or below that value.   ExampleIf you score in the 75th percentile, then 75% of the population scored lower than you.  ExampleSuppose the test scores were         22,   34,   68,   75,   79,   79,   81,   83,   84,   87,   90,   92,   96,  and  99If your score was the 75, in what percentile did you score?SolutionThere were 14 scores reported and there were 4 scores at or below yours.  We divide           4                  100%  =  29           14So you scored in the 29th percentile.  There are special percentile that deserve recognition. The second quartile (Q2) is the median or the 50th percentile The first quartile (Q1) is the median of the data that falls below the median.  This is the 25th percentile The third quartile (Q3) is the median of the data falling above the median.  This is the 75th percentile We define the interquartile range as the difference between the first and the third quartile         IQR  =  Q3 - Q1  An example will be given when we talk about Box Plots.   Box Plots Another way of representing data is with a box plot.  To construct a box plot we do the following:   Draw a rectangular box whose bottom is the lower quartile (25th percentile) and whose top is the upper quartile (75th percentile).  Draw a horizontal line segment inside the box to represent the median. Extend horizontal line segments ("whiskers") from each end of the box out to the most extreme observations. Box plots can either be shown vertically or horizontally.  The steps describe how to create a vertical box plot, while the graph below shows an example of a horizontal box plot the shows how student's commuting miles are distributed.   Back to the Elementary Statistics (Math 201) Home Page