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: Calculate the sum of \(X\) values, \(\sum X\)

\(\sum X=5 + 3+0+( - 3)+( - 5)=0\)

Step2: Calculate the sum of \(Y\) values, \(\sum Y\)

\(\sum Y=1 + 3+5+7+9 = 25\)

Step3: Calculate \(X^{2}\) for each data - point

For \(A\): \(X^{2}=5^{2}=25\); For \(B\): \(X^{2}=3^{2}=9\); For \(C\): \(X^{2}=0^{2}=0\); For \(D\): \(X^{2}=(-3)^{2}=9\); For \(E\): \(X^{2}=(-5)^{2}=25\). Then \(\sum X^{2}=25 + 9+0+9+25=68\)

Step4: Calculate \(XY\) for each data - point

For \(A\): \(XY = 5\times1=5\); For \(B\): \(XY=3\times3 = 9\); For \(C\): \(XY=0\times5 = 0\); For \(D\): \(XY=(-3)\times7=-21\); For \(E\): \(XY=(-5)\times9=-45\). Then \(\sum XY=5 + 9+0-21-45=-52\)

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

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

Step6: Calculate \((\sum Y)^{2}\)

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

Step7: Calculate \(\sum X\sum Y\)

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

Answer:

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