Question 1203687
<font color=black size=3>
Tutor @mananth is mostly correct.


The only mistake is ∑(X²Y)= 875*28 is false


We cannot say  ∑(X²Y) = ∑X²*∑Y because ∑(A*B) = ∑A*∑B isn't true.


Consider the small sets
A = {1,2,3}
B = {4,5,6}


They have these sums
∑A = 1+2+3 = 6
∑B = 4+5+6 = 15


Then,
C = A*B = pairwise multiplication
C = {1*4, 2*5, 3*6}
C = {4,10,18}
∑C = 4+10+18 = 32
But,
∑A*∑B = 6*15 = 90
which does not match with ∑C = 32


This is one counter-example to show why ∑A*∑B = ∑(A*B) is false.



This is how I would compute ∑(X²Y)
<table border = "1" cellpadding = "5"><tr><td>x</td><td>y</td><td>x^2</td><td>x^2y</td></tr><tr><td>8</td><td>1</td><td>64</td><td>64</td></tr><tr><td>9</td><td>2</td><td>81</td><td>162</td></tr><tr><td>10</td><td>3</td><td>100</td><td>300</td></tr><tr><td>11</td><td>4</td><td>121</td><td>484</td></tr><tr><td>12</td><td>5</td><td>144</td><td>720</td></tr><tr><td>13</td><td>6</td><td>169</td><td>1014</td></tr><tr><td>14</td><td>7</td><td>196</td><td>1372</td></tr></table>
I recommend using a spreadsheet.
Then we sum the items in the X²Y column:
64 + 162 + 300 + 484 + 720 + 1014 + 1372 = <font color=red>4116</font>
This value is not equal to the result of 875*28.



Therefore, ∑(X²Y) = <font color=red>4116</font>
</font>