Which is better to study data science or big data?

Data Science, AI and ML
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#1
Data science is the super-set which encompasses Big Data technologies as well; however, students specializing in Big Data & Data science have certain demarcations both in terms of the specialized skillsets they acquire & hone, as well as the opportunities & demand in the market. Both Big Data analysts as well as data scientist need to be focussed on ‘data’ – however, big data analyst should emphasize on data organizational & structuring and creating a mechanism wherein business analysts & data scientist can seamlessly access the requisite data.

Data scientist, on the other hand, focuses on application of machine learning techniques & algorithms on the accessed data to derive actionable insights. Therefore, the choice of specialization depends largely on the interest level of the candidates – a more technically blended student should progress in the field of Big Data while a more statistically inclined student should look for data science as a career prospect.
#2

Both I would say. If you are more into the math and stats aspect of analytics, data science is for you.

If you are into the engineering aspect of things like writing optimised codes, parallelisation etc. Big data is for you.

To add let me also say that these fields converge for some of us, where you have to work on both of these at the same time. With time I would daresay that there will be a need for both skills in the same person.