67 72 76 76 84 Compute the sample standard deviation s for t

67, 72, 76, 76, 84. Compute the sample standard deviation s for this data set.

Solution

Getting the mean, X,      
      
X = Sum(x) / n      
Summing the items, Sum(x) =    375  
As n =    5  
Thus,      
X =    75  
      
Setting up tables,      

      
      
Thus, Sum(x - X)^2 =    156  
      
Thus, as       
      
s^2 = Sum(x - X)^2 / (n - 1)      
      
As n =    5  
      
s^2 =    39  
      
Thus,      
      
s =    6.244997998 [ANSWER, SAMPLE STANDARD DEVIATION]