The coefficient of variation expressed as a percent is used

The coefficient of variation, expressed as a percent, is used to describe the standard deviation relative to
the mean. It allows us to compare variability of data sets with different measurement units and is
calculated as follows:
coefficient of variation = (s / x ) × 100%
Find the coefficient of variation for the following sample of weights (in pounds):
21 12 10 15 25 x = 197 and x2 = 4267
24 16 18 26 30
A) 49.9% B) 44.2% C) 33.2% D) 35.6%

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Sum(x) =    197      
As n =    10      
Thus,          
X =    19.7      
          
Setting up tables,          
x   x - X   (x - X)^2  
21   1.3   1.69  
12   -7.7   59.29  
10   -9.7   94.09  
15   -4.7   22.09  
25   5.3   28.09  
24   4.3   18.49  
16   -3.7   13.69  
18   -1.7   2.89  
26   6.3   39.69  
30   10.3   106.09  
          
          
Thus, Sum(x - X)^2 =    386.1      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    10      
          
s^2 =    42.9      
          
Thus,          
          
s =    6.549809158      
          
Also, we have          
      
coefficient of variation = s/mean*100% =    33.2477622% [OPTION C]