Question

1. for the following set of scores, find the value of each expression: a. $nsum x^{2}$ b. $(sum y)^{2}$ c. $sum xy$ d. $sum xsum y$ participant x y a 5 1 b 3 3 c 0 5 d -3 7 e -5 9

Explanation:

Step1: Determine the number of data - points

There are \(n = 5\) participants.

Step2: Calculate \(\sum X\), \(\sum Y\), \(\sum X^{2}\), and \(\sum XY\)

• \(\sum X=5 + 3+0+( - 3)+(-5)=0\)
• \(\sum Y=1 + 3+5+7+9 = 25\)
• \(X^{2}\) values for each participant: \(5^{2}=25\), \(3^{2}=9\), \(0^{2}=0\), \((-3)^{2}=9\), \((-5)^{2}=25\). So, \(\sum X^{2}=25 + 9+0+9+25 = 68\)
• \(XY\) values for each participant: \(5\times1 = 5\), \(3\times3 = 9\), \(0\times5 = 0\), \((-3)\times7=-21\), \((-5)\times9=-45\). So, \(\sum XY=5 + 9+0-21 - 45=-52\)

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

\(n\sum X^{2}=5\times68 = 340\)

Step4: Calculate \((\sum Y)^{2}\)

\((\sum Y)^{2}=25^{2}=625\)

Step5: Calculate \(\sum X\sum Y\)

\(\sum X\sum Y=0\times25 = 0\)

Answer:

a. \(340\)
b. \(625\)
c. \(-52\)
d. \(0\)