In the sub$-$section

Binary Splitting of Quantitative Attributes

of sectionTable $3\mathrm{.}3.$ A sample data for the loan borrower classification problem.

$\backslash$table$[[$Home Owner,Marital Status,Annual Income,Defaulted?,$],[1,$Yes,Single,$125000,$No$],[2,$No$,$Married,$100000,$No$],[3,$No$,$Single,$70000,$No$],[4,$Yes,Married,$120000,$No$],[5,$No$,$Divorced,$95000,$Yes$],[6,$No$,$Single,$60000,$No$],[7,$Yes,Divorced,$220000,$Yes$],[8,$No$,$Single,$85000,$No$],[9,$No$,$Married,$75000,$Yes$]]$

Is the argument valid? Elaborate your answer.

$3\mathrm{.}3\mathrm{.}3$ Measures for Selecting an Attribute Test Condition

in Tan's textbook, the authors proposed some optimization technique and concluded that

$...$ This strategy reduces the number of candidate split positions to consider from $9$ to $2$

for the dataset in Table $3\mathrm{.}1$ blow: