Question

for the following set of scores, find the value of each expression: a. $sum x^{2}$ b. $(sum x)^{2}$ c. $sum(x - 3)$ d. $sum(x - 3)^{2}$
$\begin{array}{c}x\\6\\1\\4\\5\\2end{array}$

Explanation:

Step1: Identify the data set

The data set is \(X = \{1,4,5,2\}\).

Step2: Calculate \(\sum X^{2}\)

Square each value and sum them. \(1^{2}+4^{2}+5^{2}+2^{2}=1 + 16+25 + 4=\sum X^{2}=46\).

Step3: Calculate \((\sum X)^{2}\)

First find \(\sum X=1 + 4+5+2=12\), then \((\sum X)^{2}=12^{2}=144\).

Step4: Calculate \(\sum(X - 3)\)

Subtract 3 from each value and sum. \((1 - 3)+(4 - 3)+(5 - 3)+(2 - 3)=- 2+1+2 - 1=0\).

Step5: Calculate \(\sum(X - 3)^{2}\)

Subtract 3 from each value, square the result, and sum. \((1 - 3)^{2}+(4 - 3)^{2}+(5 - 3)^{2}+(2 - 3)^{2}=(-2)^{2}+1^{2}+2^{2}+(-1)^{2}=4 + 1+4+1 = 10\).

Answer:

a. 46
b. 144
c. 0
d. 10