Compute the sample mean sample variance and sample standard

Compute the sample mean, sample variance and sample standard deviation.

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    1268      
As n =    10      
Thus,          
X =    126.8   [ANSWER, SAMPLE MEAN]

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Setting up tables,          
x   x - X   (x - X)^2  
136   9.2   84.64  
169   42.2   1780.84  
120   -6.8   46.24  
128   1.2   1.44  
129   2.2   4.84  
143   16.2   262.44  
115   -11.8   139.24  
146   19.2   368.64  
96   -30.8   948.64  
86   -40.8   1664.64  

Thus, Sum(x - X)^2 =    5301.6      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    10      
          
s^2 =    589.0666667   [ANSWER, SAMPLE VARIANCE]

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Thus,          
          
s =    24.27069564   [ANSWER, SAMPLE STANDARD DEVIATION]

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