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. σx
b. σy
c. σ(x + y)
d. σxy

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

Explanation:

Step1: Calculate $\Sigma X$

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

Step2: Calculate $\Sigma Y$

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

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

First find $X + Y$ for each participant:
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 $\Sigma(X + Y)=4 + 6+0+( - 2)+6$
$=4 + 6+0 - 2+6$
$=14$

Step4: Calculate $\Sigma XY$

First find $XY$ for each participant:
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 $\Sigma XY=3 + 5+( - 4)+( - 8)+8$
$=3 + 5-4 - 8+8$
$=4$

Answer:

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