1. **State the problem:** We have two sets of scores X and Y: | X | Y | |---|---| | 1 | 5 | | 3 | 1 | | 0 | -2 | | 2 | -4 | We need to calculate: a. $\Sigma X$ (sum of all X values) b. $\Sigma Y$ (sum of all Y values) c. $\Sigma X^2 Y$ (sum of each $X$ squared times $Y$) d. $\Sigma XY$ (sum of each $X$ times $Y$) 2. **Formulas and rules:** - $\Sigma X = x_1 + x_2 + \cdots + x_n$ - $\Sigma Y = y_1 + y_2 + \cdots + y_n$ - $\Sigma X^2 Y = \sum (X_i^2 \times Y_i)$ - $\Sigma XY = \sum (X_i \times Y_i)$ 3. **Calculate each sum:** - $\Sigma X = 1 + 3 + 0 + 2 = 6$ - $\Sigma Y = 5 + 1 + (-2) + (-4) = 0$ - Calculate each $X^2 Y$: - For $X=1, Y=5$: $1^2 \times 5 = 1 \times 5 = 5$ - For $X=3, Y=1$: $3^2 \times 1 = 9 \times 1 = 9$ - For $X=0, Y=-2$: $0^2 \times (-2) = 0 \times (-2) = 0$ - For $X=2, Y=-4$: $2^2 \times (-4) = 4 \times (-4) = -16$ - Sum these: $5 + 9 + 0 + (-16) = -2$ - Calculate each $XY$: - For $X=1, Y=5$: $1 \times 5 = 5$ - For $X=3, Y=1$: $3 \times 1 = 3$ - For $X=0, Y=-2$: $0 \times (-2) = 0$ - For $X=2, Y=-4$: $2 \times (-4) = -8$ - Sum these: $5 + 3 + 0 + (-8) = 0$ 4. **Final answers:** - a. $\Sigma X = 6$ - b. $\Sigma Y = 0$ - c. $\Sigma X^2 Y = -2$ - d. $\Sigma XY = 0$