Pseudo-label selection in semi-supervised learning is commonly driven by maximum-confidence thresholds, yet confidence alone can be unreliable under model overconfidence and class imbalance. We propose CoVar, a confidence--variance framework that assesses pseudo-label reliability by jointly modeling Maximum Confidence (MC) and Residual-Class Variance (RCV). Starting from entropy minimization, we derive a second-order cross-entropy approximation showing that low-loss pseudo-labels are favored when MC is high and RCV is low, with a confidence-dependent penalty that becomes stronger for near-certain predictions. Based on this criterion, CoVar embeds predictions into a two-dimensional confidence--variance space and uses SVD-based spectral relaxation to separate reliable and unreliable predictions without hand-tuned confidence thresholds. Cluster-wise Gaussian weighting then converts this separation into per-sample training weights. The resulting weights can be integrated into existing semi-supervised segmentation and classification pipelines during training and introduce no inference-time overhead. Experiments on PASCAL VOC 2012, Cityscapes, CIFAR-10, CIFAR-100, SVHN, and STL-10 show clear gains on VOC and Cityscapes under matched backbones, as well as competitive or improved error rates on standard classification benchmarks. These results indicate that residual-class dispersion provides a useful signal complementary to confidence for robust pseudo-label selection.