In this paper, we present "K-Means+ID3,” a method to cascade k-Means clustering and the ID3 decision tree learning methods for classifying anomalous and normal activities in a computer network, an active electronic circuit, and a mechanical mass-beam system. The k-Means clustering method first partitions the training instances into k clusters using Euclidean distance similarity. On each cluster, representing a density region of normal or anomaly instances, we build an ID3 decision tree. The decision tree on each cluster refines the decision boundaries by learning the subgroups within the cluster. To obtain a final decision on classification, the decisions of the k-Means and ID3 methods are combined using two rules: 1) the Nearest-neighbor rule and 2) the Nearest-consensus rule. We perform experiments on three data sets: 1) Network Anomaly Data (NAD), 2) Duffing Equation Data (DED), and 3) Mechanical System Data (MSD), which contain measurements from three distinct application domains of computer networks, an electronic circuit implementing a forced Duffing Equation, and a mechanical system, respectively. Results show that the detection accuracy of the K-Means+ID3 method is as high as 96.24 percent at a false-positive-rate of 0.03 percent on NAD; the total accuracy is as high as 80.01 percent on MSD and 79.9 percent on DED.