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Learning Math Home
Data Session 4, Part B: The Median and the Three-Number Summary
 
Session 4 Part A Part B Part C Part D Part E Homework
 
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Session 4, Part B:
The Median and the Three-Number Summary

In This Part: The Median | The Three-Noodle Summary | The Three-Number Summary
Even Data Sets | Review

In the previous example, it wasn't hard to find the median because there were 11 noodles -- an odd number. For an odd number of noodles, the median is the noodle in the middle. But how do we find the median for an even number of noodles?

Add a 12th noodle, with a different length from the other 11 noodles, to the original collection. Arrange the noodles in order from shortest to longest.

Problem B6

Solution  

Using the method of removing pairs of noodles (the longest and the shortest), try to determine the median noodle length. What happens?


 

This time, there won't be one remaining noodle in the middle -- there will be two! If you remove this middle pair, you'll have no noodles left.

Therefore, you'll need to draw a line midway between the two remaining noodles to play the role of the median. The length of this line should be halfway between the lengths of the two middle noodles:

Move the middle pair aside, and you can see your new median:

Notice that this median still divides the set of noodles into two groups of the same size -- the six noodles shorter than the median and the six noodles longer than the median:

The major difference is that, this time, the median is not one of the original noodles; it was computed to divide the set into two equal parts.

Note: It is a common mistake to include this median in your data set when you've added it in this way. This median, however, is not part of your data set.



video thumbnail
 

Video Segment
In this video segment, participants discuss the process of finding the median of a data set with an even number of values (in this case n = 20). Watch this video segment to review the process you used in Problem B6 or if you would like further explanation.

Note: The data set used by the onscreen participants is different from the one provided above.

If you're using a VCR, you can find this segment on the session video approximately 5 minutes and 8 seconds after the Annenberg Media logo.

 

 

Problem B7

Solution  

If you could see only the median of a set of 12, what would you know about the other noodles?


 
 

You can convert the Three-Noodle Summary for these 12 noodles to the Three-Number Summary in the same way you did it for the set of 11 noodles:

Three-Number Summary

Add a vertical number line, and mark the lengths of the three noodles:

Remove the noodles, and you're left with the Three-Number Summary:


Next > Part B (Continued): Review

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