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Learning Math Home
Data Session 4, Part E: Finding the Five-Number Summary Numerically
 
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Session 4, Part E:
Finding the Five-Number Summary Numerically (30 minutes)

In This Part: Locating the Median from Ordered Data | Calculating the Position of the Median

In Part D, we used noodles to help us visualize the concept of quartiles. In practice, however, the task of determining quartiles is treated strictly as a numerical problem. It is based on an ordered list of numerical measurements and the position of each measurement in the list. In Part E, we'll transition to this numerical approach. Note 3

Remember the procedure for determining quartiles described earlier: First find the median; then find the first and third quartile values.

Let's begin with 13 noodles, arranged in ascending order:

 

 

Each noodle has a position in this ordered list: (1) indicates the shortest noodle, (2) the next shortest, and so on. The longest noodle is (13):

 

 

The letter n is often used in statistics to indicate the number of data values in a set. In this case, there are n = 13 noodles, and 13 positions are indicated on the line above. The median is in position (7), because there are just as many positions (six) to the left of the median as there are to the right of the median:

 

The position of the median in an ordered list with n = 13 is (7). If there had been 14 items in the list, the position would have been halfway between positions (7) and (8), or (7.5). So if n = 14, the position of the median is (7.5).

Problem E1

Solution  

Find the position of the median for at least three other values of n. Then use this information to come up with a general mathematical rule for determining the position of the median if you know the number of items in an ordered list.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Try consecutive numbers, like 10, 11, and 12. To get you started, if n = 10, the median will be halfway between the fifth and sixth items, so the position of the median is (5.5).   Close Tip

Next > Part E (Continued): Calculating the Position of the Median

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