In weakly supervised anomaly behavior detection, selecting critical normal and anomalous instances from video-level labeled videos is essential for learning discriminative features that distinguish abnormal events from normal states. Existing feature selection strategies are primarily based on the anomaly intensity of individual instances, while the global statistical characteristics among instances are ignored. To address this, a joint memory and mean statistics enhanced feature selection method was proposed. In this method, global normal patterns and mean statistics were stored as anchor points, the deviation degree of input video features relative to these anchors was calculated, and positive and negative samples were selected based on the deviation magnitude. Then, a triplet loss function was constructed to constrain the samples, and the discriminative features between normal and abnormal states were enhanced through the discrimination of key samples. Furthermore, considering the ambiguity of boundaries between normal and abnormal video segments, a dynamic graph convolution module with sliding window constraints was designed to strengthen the feature representation of gradient processes and focus on local abnormal patterns. The experimental results demonstrate that AUC(area under curve) and AP(average precision) metrics of 86.25% and 83.87% are achieved by the proposed method on the UCF-Crime and XD-Violence datasets, respectively, verifying its effectiveness. It is proved that the feature selection strategy based on two global statistics of memory and mean proposed can effectively select key sample instances and significantly enhance the ability of the model to discriminate between normal and abnormal patterns.