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 rth percentile the value such that r percent of the
data fall at or below that value.
If you score in the 75th percentile, then 75% of the population scored lower than you.
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?
There were 14 scores reported and there were 4 scores at or below yours. We divide
So you scored in the 29th percentile.
There are special percentile that deserve recognition.
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.
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.