The Following Table Lists the Amounts Paid in Mortgages as a Percentage

Essay

The following table lists the amounts paid in mortgages as a percentage of the household income in the town Aponia. Calculate the variance and standard deviation of the data, if mean is given as 22.4%. The percentage (x) values are estimated as midpoints of each percentage range. $$\begin{array} { | l | l | l | } \hline \begin{array} { l } \text { Mortgage as a } \\\text { percentage of } \\\text { household income in } \\\text { Aponia }\end{array} & & \\\hline \text { Group in \% } & \begin{array} { l } \text { Percentage } \\\text { (x) }\end{array} & \begin{array} { l } \text { Number of } \\\text { households (f) }\end{array} \\\hline 0 - 10 & 5 & 4567 \\\hline 10 - 20 & 15 & 6562 \\\hline 20 - 30 & 25 & 3356 \\\hline 30 - 40 & 35 & 2975 \\\hline 40 - 50 & 45 & 1644 \\\hline 50 - 60 & 55 & 1376 \\\hline\end{array}$$