A day as a data science intern really varies. It depends on the kind of team you're on. My role was as a product data science, so I was either working on my long-term project (writing data pipelines, querying data, meeting with team members to discuss strategy) or working on short-term goals and tasks for other team members (e.g. putting together analyses of our product performance). Another data science might be working on machine learning work and have less immediate product impact.
There is no required start time or end time for me when I was working at Facebook. As a summer intern I worked on a project throughout a 3-month period. My mentor and I decided several milestones for the project and each week I had several tasks to finish to meet each milestone. Basically everyday I started to work on the most urgent or most important task I have on my task list. Sometimes I need to learn new technology or framework if necessary. The work style is pretty chill. I can work any where I want. I can take a rest any time I felt tired.
Get to work around 8 on the early shuttle. Go to gym, grab breakfast, and at my desk by around 9. Working at my desk pretty much all day with a break for lunch with my team or other interns around noon. Grab dinner before my shuttle home at 5:30. Depending on the day, there may be a team meeting or an intern event. I sometimes played ultimate frisbee after work too.