Stemplots: While the students are adding their scores, the teacher is drawing a stemplot on the board, with the stems ranging from 0 to 9, to represent the 10s unit of the total score.

As each student finishes adding, they come to the front of the room and record their score on the stemplot. Below is a sample stemplot.

0 | 0 1 7 2 0  
1 | 7 3 2      
2 | 7 4 3 8 6 4
3 | 5 7 2 1    
4 |            
5 | 6 0 2      
6 | 6          
7 |            
8 | 0          
9 |            

After all students have recorded their scores, discuss the method used to construct a stemplot.
Round Two: Repeat the above steps, with the second set of data added to the left of the stem creating a back to back stemplot.

Here is a sample back-to-back stemplot.

          0 | 0 | 0 1 7 2 0  
        2 4 | 1 | 7 3 2      
        8 2 | 2 | 7 4 3 8 6 4
    9 0 8 2 | 3 | 5 7 2 1    
9 5 5 0 0 1 | 4 |            
      7 4 6 | 5 | 6 0 2      
        0 1 | 6 | 6          
      4 7 4 | 7 |            
            | 8 | 0          
            | 9 |            

Discuss any patterns. Usually the scores are higher on the second round as strategies improve. Discuss whether the difference appears to be significant, or if the difference could be due to chance. When students study inferential statistics they will learn how to quantify this.
Extentions You could modify the rules for different classes to see if that changes the students’ strategies. For example, in class A, there may be a prize for only the highest score, while in class B prizes are offered to the top 50%. Would class A scores have a greater spread since taking a risk increases the probabilities of both winning the prize and scoring zero? How might this affect the average score for the class? And which ‘average’ would be most appropriate?

[Return to Stemplots] [Back to Greed1] [Continue]