Percentiles and Box Plots 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 r^{th} percentile the value such that r percent of the
data fall at or below that value. If you score in the 75^{th} percentile, then 75% of the population scored lower than you.
Example Suppose the test scores were 22, 34, 68, 75, 79, 79, 81, 83, 84, 87, 90, 92, 96, and 99 If your score was the 75, in what percentile did you score? Solution There were 14 scores reported and there were 4 scores at or below yours. We divide
4 So you scored in the 29^{th} percentile.
There are special percentile that deserve recognition.
We define the interquartile range as the difference between the first and the third quartile IQR = Q_{3}  Q_{1} 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:
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.
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