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Data Science plays a vital role in sciences and engineering disciplines to discover meaningful information and predict the outcome of real-world problems. Despite the significance of this field and high demand, knowledge of how to effectively provide data science research experience to STEM students is scarce. This paper focuses on the role of data science and analytics education to improve the students' computing and analytical skills across a range of domain-specific problems. The paper studies four examples of data-intensive STEM projects for supervised undergraduate research experiences (SURE) in Mechanical Engineering, Biomedical science, Quantum Physics, and Cybersecurity. The developed projects include the applications of data science for improving additive manufacturing, automating microscopy image analysis, identifying the quantum optical modes, and detecting network intrusion. The paper aims to provide some guidelines to effectively educate the next generation of STEM undergraduate and graduate students and prepare STEM professionals with interdisciplinary knowledge, skills, and competencies in data science. The paper includes a summary of activities and outcomes from our research and education in the field of data science and machine learning. We will evaluate the student learning outcomes in solving big data interdisciplinary projects to confront the new challenges in a computationally-driven world.