Question

for the following set of scores, find the value of each expression: a. $sum(x - 4)^2$ b. $(sum x)^2$ c. $sum x^2$ d. $sum(x + 3)$
$\begin{array}{c}x\\-1\\-3\\6\\-4end{array}$

Explanation:

Step1: Identify the scores

The scores are $X = - 1,-3,6,-4$.

Step2: Calculate $\sum(X - 4)^2$

First, find $X-4$ for each score:
For $X=-1$, $-1 - 4=-5$, $(-5)^2 = 25$;
For $X=-3$, $-3 - 4=-7$, $(-7)^2 = 49$;
For $X = 6$, $6 - 4=2$, $2^2 = 4$;
For $X=-4$, $-4 - 4=-8$, $(-8)^2 = 64$.
Then $\sum(X - 4)^2=25 + 49+4 + 64=142$.

Step3: Calculate $(\sum X)^2$

$\sum X=-1+( - 3)+6+( - 4)=-2$, so $(\sum X)^2=(-2)^2 = 4$.

Step4: Calculate $\sum X^2$

For $X=-1$, $(-1)^2 = 1$;
For $X=-3$, $(-3)^2 = 9$;
For $X = 6$, $6^2 = 36$;
For $X=-4$, $(-4)^2 = 16$.
Then $\sum X^2=1 + 9+36 + 16=62$.

Step5: Calculate $\sum(X + 3)$

For $X=-1$, $-1 + 3=2$;
For $X=-3$, $-3 + 3=0$;
For $X = 6$, $6 + 3=9$;
For $X=-4$, $-4 + 3=-1$.
Then $\sum(X + 3)=2+0 + 9+( - 1)=10$.

Answer:

a. $142$
b. $4$
c. $62$
d. $10$