The amounts of vitamin c in milligrams for 100 g 357 ounces

The amounts of vitamin c (in milligrams) for 100 g (3.57 ounces) of various randomly selected fruits and vegetables are listed. Is there sufficient evidence to conclude that the standard deviation differs from 12 mg?


7.9, 16.3, 12.8, 13.0, 32.2, 28.1, 46.4, 53.0, 15.4, 18.2, 25.0, 5.2, 34.4

I would like to know how to calculate the S i know the s will be 14.60 but i wanna know how do you get that 14.60! ive been trying to calculate but its totally a different number evo though i made sure that im doing it correctly !

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    307.9      
As n =    13      
Thus,          
X =    23.68461538      
          

Setting up tables,

          
Thus, Sum(x - X)^2 =    2560.656923      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    13      
          
s^2 =    213.3880769      
          
Thus,          
          
s =    14.60780877 [ANSWER]