Answer
The estimated value of the poverty threshold for a family of four with two children under the age of $18$ in $2008$ is $21142$.
The actual poverty threshold is $\$692$ off of the calculated value.
Work Step by Step
From the information, let ${{P}_{1}}=(2003,18660)$ and${{P}_{2}}=(2013,23624)$.
By the midpoint formula, the coordinate of the midpoint of two points ${{P}_{1}}=(2003,18660)$ and ${{P}_{2}}=(2013,23624)$ is
$\left( x,\,y \right)=\left( \frac{2003+2013}{2},\,\frac{18660+23624}{2} \right)$
$\left( x,\,y \right)=\left( \frac{4016}{2},\,\frac{42284}{2} \right)$
$\left( x,\,y \right)=\left( 2008,\,21142 \right)$
The estimated value of the poverty threshold for a family of four with two children under the age of $18$ in $2008$ is $21142$.
The actual poverty threshold in $2008$ is $\$21,834$.
Therefore, the error in estimation is:
$=|\operatorname{Actual}\,\operatorname{value}\,-\,estimated\,value|$
$=|21834-21142|\,=\,692$
Therefore, the error in estimation is $692$.
