Voltage-to-power sensitivities play a key role in the control and operation of distribution networks. To estimate these sensitivities without network information, data-driven estimation methods have been studied. However, conventional methods do not consider mutual dependency (MD) of the sensitivities and thus the estimation can be inaccurate. Thus, this paper proposes a new data-driven estimation method of the sensitivities, which considers MD of the sensitivities in medium voltage distribution networks. In the proposed method, via MD analysis, the sensitivities are estimated by solving nonlinear least square problems and thus the accurate estimation can be achieved. The effectiveness of the proposed method is verified using the real-time platform.