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

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

Transcript text: 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. $(\Sigma X) (\Sigma Y)$ Subtract $X$ from $Y$ and sum the differences. $\Sigma(Y-X)$ Sum the X scores. $\Sigma X$

Solution

Solution Steps

Step 1: Sum of Products

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

Step 2: Product of Sums

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: \[ \left( \sum_{i=1}^{n} X_i \right) \left( \sum_{i=1}^{n} Y_i \right) = 6 \cdot 15 = 90 \]

Step 3: Sum of Differences

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