Differential privacy is a confidentiality metric and quantitatively guarantees the confidentiality of individuals. A noise criterion, called sensitivity, must be calculated when constructing a probabilistic disturbance mechanism that satisfies differential privacy. Depending on the statistical process, the sensitivity may be very large or even impossible to compute. As a result, the usefulness of the constructed mechanism may be significantly low; it might even be impossible to directly construct it. In this paper, we first discuss situations in which sensitivity is difficult to calculate, and then propose a differential privacy with additional dummy data as a countermeasure. When the sensitivity in the conventional differential privacy is calculable, a mechanism that satisfies the proposed metric satisfies the conventional differential privacy at the same time, and it is possible to evaluate the relationship between the respective privacy parameters. Next, we derive sensitivity by focusing on correlation coefficients as a case study of a statistical process for which sensitivity is difficult to calculate, and propose a probabilistic disturbing mechanism that satisfies the proposed metric. Finally, we experimentally evaluate the effect of noise on the sensitivity of the proposed and direct methods. Experiments show that privacy-preserving correlation coefficients can be derived with less noise compared to using direct methods.