Actuarial science involves the study of insurance related activities. On the other hand data science is a study of types of data sets and their relationships and analysis.
Actuarial is all about finance type things (insurance, modeling, investment, etc.). Data science, on the other hand, has a lot of far ranging definitions. I teach a data science curriculum, and I cover aspects in databases, informatics, data mining, machine learning, data visualization, GIS, and many other types of areas. Data science skills are great to have in actuarial practice, but one does not need them necessarily to be an actuary.
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