Calculate the sum of products of deviations (SP) for the following set of scores. Use the definitional formula and then the computational formula. Verify that you get the same answer with both formulas.
X  Y 
0  1 
4  3 
5  3 
2  2 
4  1 
To calculate: The sum of products of deviations (SP) and verify if the answer is the same if computed by definitional formula and computational formula.
Given Info:
Following set of scores are given:
X  Y 
0  1 
4  3 
5  3 
2  2 
4  1 
15  10 
Calculation:
The definitional formula for SP is:
Where





0  1  3  1  3 
4  3  1  1  1 
5  3  2  1  2 
2  2  1  0  0 
4  1  1  1  1 

Thus, SP value by using definitional formula is
The computational formula is:
X  Y  XY 
0  1  0 
4  3  12 
5  3  15 
2  2  4 
4  1  4 
15  10  35 
Thus, SP value by using computational formula is
Thus, value of SP is same for both formulas.
Sum of product deviation (SP):
Sum of products of deviations (SP) is given by
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