Question

1. two scores, x and y, are recorded for each of n = 5 participants. for these scores, find the value of each expression.

a. $sigma x$
b. $sigma y$
c. $sigma(x + y)$
d. $sigma xy$

participant	x	y
b	1	5
c	-2	2
d	-4	2
e	2	4

Explanation:

Step1: Calculate $\Sigma X$

Sum of $X$ - values: $3 + 1+( - 2)+( - 4)+2=0$

Step2: Calculate $\Sigma Y$

Sum of $Y$ - values: $1 + 5+2+2+4 = 14$

Step3: Calculate $\Sigma(X + Y)$

First find $X + Y$ for each pair:
For A: $3 + 1=4$; For B: $1 + 5 = 6$; For C: $-2+2 = 0$; For D: $-4 + 2=-2$; For E: $2+4 = 6$
Then sum them up: $4+6 + 0+( - 2)+6=14$

Step4: Calculate $\Sigma XY$

Find $XY$ for each pair:
For A: $3\times1 = 3$; For B: $1\times5 = 5$; For C: $-2\times2=-4$; For D: $-4\times2=-8$; For E: $2\times4 = 8$
Then sum them up: $3 + 5+( - 4)+( - 8)+8=4$

Answer:

a. $0$
b. $14$
c. $14$
d. $4$