For the following set of scores 4124 a Calculate X and X2 b

For the following set of scores:

4,1,2,4

(a) Calculate X and X².

(b) Use the two sums from part (a) and the computational formula to compute SS for the scores. (Use 2 decimal places.)

Solution

a)

Consider:

Thus, Sum(x) = 11

Sum(x^2) = 37 [answers]

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b)

Now,

SS = Sum(x^2) - Sum(x)^2/n

As n = 4,

SS = 37 - 11^2/4 = 6.75 [ANSWER]

Using

SS = Sum[(x - X)^2],

Getting the mean, X,      
      
X = Sum(x) / n      
Sum(x) =    11  
As n =    4  
Thus,      
X =    2.75  
      
Setting up tables,      
x   x - X   (x - X)^2
4   1.25   1.5625
1   -1.75   3.0625
2   -0.75   0.5625
4   1.25   1.5625
      
      
Thus, Sum(x - X)^2 =    6.75 [ANSWER]