The theoretical grading G (scattered data points) derived (by Eqs. 1 and 2) from mammographic data of 31 prospective patients, who were selected at random in a double-blind mode and were classified pathologically as benign (grade 0) or malignant (grades 1 to 3) with increasing malignancy. Solid horizontal line L0∼1 refers to the pathologically grading boundary between benign grade 0 and malignant grade 1. Dash horizontal lines L1∼2, L2∼3 represents the pathologically grading boundaries between grades 1 and 2, grades 2 and 3, respectively. Error bars were obtained by the difference of theoretical grading Gt and pathological grading Gp, namely, Abs(Gt−Gp)/2, where Abs() is a mathematical function to obtain an absolute value. Boxed data points are those mismatched between theoretical and pathological grading. To protect the privacy of investigated patients, only case numbers of patients are listed