The marketing department of a riding mower manufacturer wants to understand who are more likely to buy their riding mowers. A group of data analysts is building a classification tree to classify its customers into two classes: nonowners (class 0) and owners (class 1) of riding mowers. Each customer is described by two attributes: income and lot size. The data analysts have agreed to split a set of training records (denoted by A) using customers lot size. Two subsets of records (denoted by A1 and A2 respectively) are produced after splitting A. The number of nonowners and owners in A, A1, and A2 are given below.

	A	A1	A2
Number of Nonowners	56	49	7
Number of Owners	104	44	60

Round your answers to 3 digits after the decimal point.

The entropy of A is?

The entropy of A1 is?

The entropy of A2 is?

The combined entropy of A1 and A2 is?

The reduction in entropy if training records are split using customers lot size is?

THE ANSWERS POSTED BELOW ARE WRONG:

A A1 A2 No. of Nonowners 56 49 7 No. of Owners 104 44 60 Proportion of Nonowners (p0) 0.350 0.527 0.104 Proportion of Owners (p1) 0.650 0.473 0.896 Entropy 0.934 0.998 0.483 Combined Entropy 0.934 Reduction in Entropy -0.064 0.451 Now, from the above table,

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