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Data Session 4, Part C: Quartiles and the Five-Number Summary
 
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Session 4, Part C:
Quartiles and the Five-Number Summary

In This Part: Quartiles | More Five-Number Summaries | Review

In the previous example, there were 12 noodles. Twelve is a convenient number of data values for introducing quartiles, because it is an even number and it is divisible by four. In this case, the quartiles separate the data into groups that each contain three values.

Quartiles always produce four groups of data with an equal number of data values in each group. But when the total number of data values is not divisible by four, it's trickier to determine exactly how many values will be in each of the four groups.

Determining quartiles is a two-step process:

 

First, find the median, or Med. Med divides the ordered data into two groups of equal size. One group contains data values to the left of Med, and the other contains data values to the right of Med.

 

Next, find the median of the data values to the left of Med, which is the first quartile (Q1). Similarly, the third quartile (Q3) is the median of the data values to the right of Med.

Let's illustrate how this works for 13 data values (i.e., noodles). Since the total number of noodles is now odd, the median will be one of the original 13 noodles. Note that there is the same number of noodles to the left of Med as there is to the right of Med. Since you cannot divide the 13 noodles into two equal groups without splitting a noodle, take one noodle in the middle as the median and divide the other 12 noodles into two equal groups. This will occur whenever there is an odd number of noodles. The two equal groups will have exactly half of the noodles, with one noodle left in the middle as the median.

Now we find Q1, the median of the six noodles to the left of Med, and Q3, the median of the six noodles to the right of Med. Because there is an even number of noodles to the left and right of Med, Q1 and Q3 will be represented by lines between a pair of noodles.

Note that there are three noodles to the left of Q1, three noodles between Q1 and Med, three noodles between Med and Q3, and three noodles to the right of Q3. Also note that each group of three noodles is approximately one-fourth of the total of 13 noodles. As with the calculation of the median, the quartiles split each half of the noodles into two equal groups; if there is an odd number of noodles in a half, one will be left in the middle as the quartile.


Next > Part C (Continued): Review

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