Electric Vehicle (EV) is becoming a viable and popular option, but the acceptance of the technology can be challenging and lead to an elevated driving stress. The existing studies on stress of vehicle driving has been mainly limited to the non-EVs or survey analysis. In this research, EV driving data of 40 subjects is analyzed, where each subject was asked to drive an EV over a 53 km course in a suburban city of South Korea. Physiological data including electroencephalogram (EEG) and eye-gazing were obtained along with vehicle operational data such as state of charge, altitude, and speed. The dataset was rich in information, but individual difference and nonlinear patterns made it extremely difficult to draw meaningful insights. As a solution, an information-theoretic framework is proposed to evaluate mutual information between physiological and operational data as well as the entropy of physiological data itself. The result shows two groups of subjects, one not showing much evidence of stress and the other exhibiting sufficient stress. Among the subjects who showed sufficient driving stress, 9 out of the top 10 high EEG-entropy drivers were female, one driver showed a strong pattern of range anxiety, and several showed patterns of uphill climbing anxiety.