Question

Used data below to complete the following calculations m=65,37,6,

Answer 1

we are given a data set and we are asked to determine the following operations:

`\sum ^{}_{}mf`

To determine this, we need to add the products of each of the values of "m" and "f", like this:

`\sum ^{}_{}mf=m_1f_1+m_2f_2+m_3f_3+m_4f_4+m_5f_5`

Replacing the values:

`\sum ^{}_{}mf=(65)(8)_{}+(37)(75)+(6)(21)+(67)(34)+(18)(26)`

Solving the operation:

`\sum ^{}_{}mf=6167`

Now we are asked to determine the following operation:

`\sum ^{}_{}m^2f`

Now we need to add the product of the squares of "m" by "f", like this:

`\sum ^{}_{}m^2f=m^2_1f_1+m^2_2f_2+m^2_3f_3+m^2_4f_4+m^2_5f_5`

replacing the values:

`\sum ^{}_{}m^2f=(65)^2(8)_{}+(37)^2(75)+(6)^2(21)+(67)^2(34)+(18)^2(26)`

Solving the operations we get:

`\sum ^{}_{}m^2f=298281`

Now we are asked to solve the following operation:

`\sum ^{}_{}(m^{}f)^2=(m_1f_1)^2+(m_2f_2)^2+(m_3f_3)^2+(m_4f_4)^2+(m_5f_5)^2`

Replacing the values we get:

`\sum ^{}_{}(m^{}f)^2=((65)(8)_{})^2+((37)(75))^2+((6)(21))^2+((67)(34))^2+((18)(26))^2`

Solving we get:

`\sum ^{}_{}(m^{}f)^2=13395209`