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Statistics graduates are especially sought by analytics firms. E.g. - Mu Sigma, Fractal Analytics, EXL and others. However, many firms would require you to have done a Masters in the subject as well. You would have a distinct advantage over most engineers whom analytics firms find available as they will not be as well versed with statistical models and techniques.
For a Masters you can especially aim to get one from ISI (Indian Statistical Institute) Delhi/Kolkata, which is an advanced research institute and also an Institute of National Importance like the IITs and NITs. At ISI, you'll be taught by world-class faculty and also get a highly competitive peer group.
If you wish to do an MBA to make a career in the private sector, the IIMs would love to have you if you have a good academic record as you'll provide the much needed diversity to the engineer heavy b-school crowd. A Statistics background could help you differentiate yourself in front of the recruiters as well!
Lastly, if you do earn an M.Stat degree, you would be eligible for a career in Indian Statistical Services, whose exam is conducted by UPSC every year.
You certainly have a lot to look forward to.
P.S. At DU, try to get at least 70% marks and most of all try to assimilate whatever theories you learn so that you can apply them to real world problems. This would help you in the long run as you would be more likely to enjoy the subject yourself and express enthusiasm while talking about your subject in interviews or while writing SOPs.

Mumbai and Pune have a large number of branches of NIIT. However, now that NIIT provides an online platform with courses that are just as prominent, distance is no longer an impediment. It's also worth mentioning my own personal experiences with online education. When I was looking for a school to help me further my career, I had a Full Stack Digital Marketing on my wish list. Because I wanted to ensure that I was investing my time and money correctly, I chose an institution with a good reputation. NIIT was the best option for me because of its large variety of courses. A variety of educational options are provided to ensure that students fully comprehend the subject matter. This institutes curriculum, in my opinion, covers all you need to know to be successful in this industry. Students profit immensely from this method since the majority of their sessions are personalised to match their unique needs. Provide an authentic certification from an authorised source is a good idea, according to me. To ensure that you can put your new skills to use right away, the training will finish with a job offer in place.