This study proposes and examines an analytical method with the aim of improving the quality of education and learning by situating the answers to full descriptive questions in probability and statistics to make variables of learners' comprehension of learned content as answer characteristics, based on actual student mistakes. First, we proposed and examined a method for extracting answer characteristics from the answers to the questions in probability and statistics as variables. Second, we proposed a method for obtaining answer characteristics to accurately describe learners' comprehension of each problem and indicate learning and educational policies for learners to improve learning by using regression trees. In addition, the relationship between learners' general ability and answer characteristics was visualized in an item characteristic chart to indicate the general comprehension of the learners. Further, the relationship between learners' learning strategy and answer characteristics was structuralized using Bayesian network models, and effective learning strategies for both learners as a whole and individual learners were extracted and evaluated towards the qualitative improvement of their comprehension using probabilistic reasoning. Our findings showed that the effectiveness of a learning strategy varies with each concept treated in a given problem; with the degree of basical or applied answer characteristics, indicating that the required learning strategy varies according to a given learner's stage of learning. Moreover, the improvement of hours studying dispersion for both mid-term and final examinations was revealed as effective for a wide range of subjects.