CHAPTER 14 Quartiles, Deciles, Percentiles, and Boxplots

Here is our homerun data set:

35 26 46 24 24 22 35 54 12 25 16 26 11 31 16 28 17 20 25 18 20 27 17 0 12 24 16 31 7 6 25 20 20 21 23 7 7 7 12 21

If I sort this data set, it looks like this:

0 6 7 7 7 7 11 12 12 12 16 16 16 17 17 18 20 20 20 20 21 21 22 23 24 24 24 25 25 25 26 26 27 28 31 31 35 35 46 54

The first quartile of this data set is the number that has approximately 25% of the data to its left. In R, it can be obtained by typing

quantile(homeruns, .25).

Similarly, the second quartile is the number that has approximately 50% of the data to its left, and the third quartile is the number that has approximately 75% of the data to its left. In R, each can be obtained, respectively, by typing

quantile(homeruns, .50) and quantile(homeruns, .75).

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If you would like to quickly compute all three quartiles at once, type

quantile(homeruns).

This produces the following output:

0% 25% 50% 75% 100%

0.00 15.00 20.50 25.25 54.00

The middle three numbers are the quartiles.

Deciles divide the data set into ten pieces. The 3rd decile, for instance, is the num-ber that has 30% of the data to its left. It can be obtained by typing

quantile(homeruns, .30).

Similarly, the 8thdecile, for instance, can be obtained by typing

quantile(homeruns, .80).

Finally, percentiles divide the data set into one hundred pieces. The 30th percentile, for instance, is the number that has 30% of the data to its left. It can be obtained by typing

quantile(homeruns, .30).

Similarly, the 5th percentile, for instance, is the number that has 5% of the data to its left, and it can be obtained by typing

quantile(homeruns, .05).

There is a type of graph associated with the quartiles. It is called a boxplot. To generate a boxplot in R, type

boxplot(homeruns).

In R the following output is generated:

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The bottom edge of the box is located at the first quartile, the middle line inside the box is located at the second quartile, and the top edge of the box is located at the third quartile. The dots that you see plotted above represent outliers. The exten-sions of the plot go out to the largest and smallest data values which are not outli-ers.

Here is a video tutorial:

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CHAPTER 14 Quartiles, Deciles, Percentiles, and Boxplots