Answer the following questions based on this sample of stude

Answer the following questions based on this sample of student scores: 85,62,81,72,75,45

Find mean, find the standard deviation of the data

What is the z-score for a student who scored a 62? would 62 be considered unusual?

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    420      
As n =    6      
Thus,          
X =    70   [ANSWER, MEAN]

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Setting up tables,          
x   x - X   (x - X)^2  
85   15   225  
62   -8   64  
81   11   121  
72   2   4  
75   5   25  
45   -25   625  
          
Thus, Sum(x - X)^2 =    1064      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    6      
          
s^2 =    212.8      
          
Thus,          
          
s =    14.58766602   [ANSWER, STANDARD DEVIATION]

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z = (x - X)/s = (62-70)/14.58766602 = -0.548408497 [ANSWER, Z SCORE]

As |z| < 2, then IT IS NOT UNUSUAL. [CONCLUSION]