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

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

Use the following Interactive Activity to review how you identify the Five-Noodle Summaries of a set of 13 and a set of 12 noodles.

Problem C5

  

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version, review how you would find the Five-Noodle Summary using a set of 12 noodles and a set of 13 noodles.


 

Problem C6

Solution  

Explain how you would create a Five-Noodle Summary for 14 noodles. How many noodles are in each of the four groups?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Remember that the median of a group may be represented by a noodle or by a line drawn halfway between two noodles. Since a quartile is the median of half the data, it may also be represented by a noodle or by a line drawn halfway between two noodles.   Close Tip

 

Problem C7

Solution  

Explain how you would create a Five-Number Summary for 15 noodles. How many numbers are in each of the four groups?


Take it Further

Problem C8

Solution

How many numbers are in each of the four groups if you started with 57 noodles? With 112 noodles? Can you find a rule that would allow you to determine the number of values in each group without creating a Five-Number Summary?


 

 
 

In general, the Five-Number Summary divides ordered numeric data into four groups, with each group having the same number of data values. If you know only the Five-Number Summary (Min, Q1, Med, Q3, and Max), these five values still give you a lot of information:

 

All the data values are between Min and Max.

 

Med divides the ordered data into two groups, with an equal number of values (approximately half) in each group:

 

One group contains data values to the left of Med.

 

One group contains data values to the right of Med.

 

The quartiles divide the ordered data into four groups, with an equal number of values (approximately one-fourth) in each group:

 

One group contains values to the left of Q1 (and includes Min).

 

One group contains values between Q1 and Med.

 

One group contains values between Med and Q3.

 

One group contains values to the right of Q3 (and includes Max).


 

Problem C9

Solution  

What information is learned from the interquartile range, the length of the interval between Q1 and Q3? Think about why this might be useful in describing the variation in your data.


Next > Part D: The Box Plot

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