Questions: Use summation notation to express the following calculations. Multiply scores X and Y and then add each product. EXY Sum the scores X and sum the scores Y and then multiply the sums. (ΣX) (ΣY) Subtract X from Y and sum the differences. Σ(Y-X) Sum the X scores. ΣX

Solution Steps

To find the sum of the products of corresponding scores $X$ and $Y$, we calculate: $$\sum_{i=1}^{n} X_i Y_i = 1 \cdot 4 + 2 \cdot 5 + 3 \cdot 6 = 4 + 10 + 18 = 32$$

Next, we compute the sum of the scores in $X$ and $Y$ separately, and then multiply these sums: $$\sum_{i=1}^{n} X_i = 1 + 2 + 3 = 6$$ $$\sum_{i=1}^{n} Y_i = 4 + 5 + 6 = 15$$ Thus, the product of the sums is: $$\left( \sum_{i=1}^{n} X_i \right) \left( \sum_{i=1}^{n} Y_i \right) = 6 \cdot 15 = 90$$

Finally, we find the sum of the differences between corresponding scores $Y$ and $X$: $$\sum_{i=1}^{n} (Y_i - X_i) = (4 - 1) + (5 - 2) + (6 - 3) = 3 + 3 + 3 = 9$$

Final Answer