we are given a data set and we are asked to determine the following operations:
[tex]\sum ^{}_{}mf[/tex]To determine this, we need to add the products of each of the values of "m" and "f", like this:
[tex]\sum ^{}_{}mf=m_1f_1+m_2f_2+m_3f_3+m_4f_4+m_5f_5[/tex]Replacing the values:
[tex]\sum ^{}_{}mf=(65)(8)_{}+(37)(75)+(6)(21)+(67)(34)+(18)(26)[/tex]Solving the operation:
[tex]\sum ^{}_{}mf=6167[/tex]Now we are asked to determine the following operation:
[tex]\sum ^{}_{}m^2f[/tex]Now we need to add the product of the squares of "m" by "f", like this:
[tex]\sum ^{}_{}m^2f=m^2_1f_1+m^2_2f_2+m^2_3f_3+m^2_4f_4+m^2_5f_5[/tex]replacing the values:
[tex]\sum ^{}_{}m^2f=(65)^2(8)_{}+(37)^2(75)+(6)^2(21)+(67)^2(34)+(18)^2(26)[/tex]Solving the operations we get:
[tex]\sum ^{}_{}m^2f=298281[/tex]Now we are asked to solve the following operation:
[tex]\sum ^{}_{}(m^{}f)^2=(m_1f_1)^2+(m_2f_2)^2+(m_3f_3)^2+(m_4f_4)^2+(m_5f_5)^2[/tex]Replacing the values we get:
[tex]\sum ^{}_{}(m^{}f)^2=((65)(8)_{})^2+((37)(75))^2+((6)(21))^2+((67)(34))^2+((18)(26))^2[/tex]Solving we get:
[tex]\sum ^{}_{}(m^{}f)^2=13395209[/tex]