Math  /  Data & Statistics

QuestionFind the information gain by splitting the dataset using Age? \begin{tabular}{|c|c|c|c|c|c|} \hline \#\# & Age & Prescription & Astigmatism & Rate & \begin{tabular}{l} Lenses \\ (Class) \end{tabular} \\ \hline 1 & Young & Myope & No & Reduced & None \\ \hline 2 & Young & Myope & Yes & Normal & Hard \\ \hline 3 & Young & Hypermetrope & No & Reduced & None \\ \hline 4 & Young & Hypermetrope & Yes & Reduced & None \\ \hline 5 & Young & Hypermetrope & Yes & Normal & Hard \\ \hline 6 & Young & Myope & No & Reduced & None \\ \hline 7 & Middle & Myope & Yes & Reduced & None \\ \hline 8 & Middle & Myope & Yes & Normal & Hard \\ \hline 9 & Middle & Hypermetrope & No & Normal & Soft \\ \hline 10 & Middle & Hypermetrope & Yes & Reduced & None \\ \hline 11 & Middle & Hypermetrope & Yes \square & Normal & None \\ \hline 12 & Middle & Myope & No $\$ & Reduced & None \\ \hline 13 & Middle & Myope & No & Normal & None \\ \hline 14 & Senior & Myope & Yes & Reduced & None \\ \hline 15 & Senior & Myope & Yes & Normal & Hard \\ \hline 16 & Senior & Hypermetrope & No & Reduced & None \\ \hline 17 & Senior & Hypermetrope & No & Normal & Soft \\ \hline \end{tabular}

Studdy Solution
Compute the information gain by subtracting the weighted average entropy from the original entropy.
IG(S,Age)=H(S)Hweighted IG(S, \text{Age}) = H(S) - H_{\text{weighted}}
IG(S,Age)=1.3351.1800.155 IG(S, \text{Age}) = 1.335 - 1.180 \approx 0.155
Solution: The information gain by splitting the dataset using Age is approximately 0.155.

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