interview question- As a Scrum master , what did you do to improve the team performance and what metrics did you use to do it.

Scrum Masters don't improve team performance.  The team improves it own performance. Scrum Masters ensure that the entire organization is able to understand and appreciate the Scrum framework. It sounds like the interviewer could use some help from the Scrum Master. 

I'd probably say something like this, before being escorted out:

"The key measure of progress is Done, finished increments of working product. I help organizations like yours to understand that. Sometimes, they are then willing to improve."

I agree with the previous speakers, but I know the problem.  Metrics from Evidence-Based Management can give the PO an indication if you are hitting all the quality criteria, for example. EBM helps to get a holistic view on the product. Sometimes you can get "Blind Spots" - even with Scrum, if you don't integrate much perspectives in your backlog. 

I would recommend using a Sprint Burndown chart. This a very useful tool as a Scrum Master, it gives the Scrum Master visual depiction of the progress of each sprint regarding the teams progress. If progress is slow it helps bring awareness to the team on where improvement is needed. 

As alluded to in the above comments, it's important to decouple the metrics = improvement mentality represented in the interview question.  Metrics document performance.  As such, they could be considered a tool which can help the team improve, but they're certainly not the only tool.

It's also important to understand that metrics aren't just for managers.  Understand which metrics the management team wants, but also work with your team to determine what metrics they find useful to review in order to promote their own improvement.

Further to all comments, in my opinion metrics are important however, metrics are not used for the sake of it, a gap analysis should be conducted as metric serve a particular purpose depending on each team circumstances.

@Santosh, share a story, what was the team situation, what are you tasked with, what action did you take and what was the result within the context of your observation in the team or a team to be. 

@Agile Principle 7, The primary measurement of progress is a working software, you can have some metrics towards this as an example if your team is not delivering an MVP. 

A Velocity chart, possible a bar graph of story points per sprint, should give a good enough measure over time. (All stories and issues in the sprint assumed story pointed, but other methods can work also.)

On team performance improvement, in my opinion the number 1 recomendation is to allow the team to make the best decisions they see fit; let the team find the solution. 

Then some thoughts:

• limit work in progress
• try to influence PO's not to switch in and out of tasks
• define the minimum viable product and deliver incrementally on the MVP - improving on each increment or iteration.