A school district is considering where in town to house its central office (The office must also be located at an existing school for cost reasons). If there are five schools in the district, with locations and size given in the following table, use the COG method to determine at which school the central office should be placed to minimize the average distance between the office and students.
$2,17500\begin{array} { | l | l | l| } \hline \text { Location } &\text { L,Y } & \begin{array} { l } \text { Size } \\\text { (Enrollment) }\end{array} \\\hline \text { A } & 5,5 & 2500 \\\hline \text { B } & 0,5 & 1000 \\\hline \text { C } & 0,0 & 10000 \\\hline \text { D } & 5,0 & 4500 \\\hline \text { E } & 2,1 & 7500 \\\hline\end{array}$

Question

A school district is considering where in town to house its central office (The office must also be located at an existing school for cost reasons). If there are five schools in the district, with locations and size given in the following table, use the COG method to determine at which school the central office should be placed to minimize the average distance between the office and students.

2,17500\begin{array} { | l | l | l| } \hline \text { Location } &\text { L,Y } & \begin{array} { l } \text { Size } \\\text { (Enrollment) }\end{array} \\\hline \text { A } & 5,5 & 2500 \\\hline \text { B } & 0,5 & 1000 \\\hline \text { C } & 0,0 & 10000 \\\hline \text { D } & 5,0 & 4500 \\\hline \text { E } & 2,1 & 7500 \\\hline\end{array}

Regina Givens · Accepted Answer

Final Answer :

The total number of students is (2500 + 1000 + 10000 + 4500 + 7500) = 25500
X = (5 × 2500 + 0 × 1000 + 0 × 10000 + 5 × 4500 + 2 × 7500)/25500 = 1.96
Y = (5 × 2500 + 5 × 1000 + 0 × 10000 + 0 × 4500 + 1 × 7500)/25500 = .98
Rounding these gives ( X,Y) of (2,1) which is closest to school E.

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