I agree with Vlad, it is totally fine to ask for one minute to read a graph before moving to the analysis. After you took some time you should:
- Summarize what the graph is about
- Restate the main question you have to answer
- Provide an analysis related to the question
- Provide a conclusion for the graph which answers the original question
- Present the next steps to follow based on such conclusion
That doesn’t mean that reading the graph right after you receive it is wrong – it just requires more experience and better communication skills to go through. In particular, I noticed that when people don’t take time at the beginning in a graph analysis, they often start to read it and then freeze when they read something they do not understand. This is not good, as the interviewer will assume you could freeze as well in front of a client. Thus in general if you feel uncomfortable with complex graph analysis I would suggest to ask for some time as first step – your following reading and analysis will be a lot better. The same reasoning is true for the final conclusion (unless the interviewer explicitly requests a 10-second one).
Finally, be aware that when you ask for some time to organize your thoughts, the interviewer could sometimes request to provide an immediate response to put you under pressure; if that happens, the best thing is to repeat the original question/information to gain some time, then move through the reading/analysis that you have to provide.