John listens to a variety of music, including easy listening, classical, and pop

Question

John listens to a variety of music, including easy listening, classical, and pop/rock. These are the lengths of some of his favorite albums for each of these categories:

Easy Listening         Classical         Pop/Rock

39                               67                   47

60                               76                   47

40                               51                   66

56                               51                   50

41                               36                   78

55                                                      61

41

What is the standard deviation of the "easy listening" data set?

Explanation / Answer

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    332      
As n =    7      
Thus,          
X =    47.42857143      
          
Setting up tables,          
x   x - X   (x - X)^2  
39   -8.428571429   71.04081633  
60   12.57142857   158.0408163  
40   -7.428571429   55.18367347  
56   8.571428571   73.46938776  
41   -6.428571429   41.32653061  
55   7.571428571   57.32653061  
41   -6.428571429   41.32653061  
          
Thus, Sum(x - X)^2 =    497.7142857      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    7      
          
s^2 =    82.95238095      
          
Thus,          
          
s =    9.107819769   [ANSWER]  

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