Imagine that a researcher wanted to know the average weight

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What’s the sample standard deviation? (show work)

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    547      
As n =    5      
Thus,          
X =    109.4      
          
Setting up tables,          
x   x - X   (x - X)^2  
120   10.6   112.36  
99   -10.4   108.16  
101   -8.4   70.56  
87   -22.4   501.76  
140   30.6   936.36  
          
Thus, Sum(x - X)^2 =    1729.2      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    5      
          
s^2 =    432.3      
          
Thus,          
          
s =    20.79182532   [ANSWER]