Binary Splitting of Quantitative Attributes

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n the sub$-$section

Binary Splitting of Quantitative Attributes

of section

$3\mathrm{.}3\mathrm{.}3$ 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 $3\mathrm{.}1$ blowlow:

Is the argument valid? Elaborate your answer.