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Higher studies options after B.Sc in Statistics
M.Sc Actuarial science
M.Sc. in Library and Information Science
M.Sc. in Quantitative Economics
MCA
Masters in Math
Masters in Statistics
MBA
P.G. Diploma in Stat. Methods with Applications
Specialist Development Program in SQC
JRF & SRF Rules
Junior/Senior Research Fellowship
Other certification courses after B.Sc in Statistics
Certificate/Diploma course in Computer Programming & Applications#
Part-time Certificate/Diploma course in SQC
Intensive course in Programming and Application of Electronic Computers *
Part-time course in Statistical Methods and Applications**
Part-time course in SQC
Career scope after B.Sc in Statistics
Students with a degree in B.Sc. Statistics are eligible to apply for various jobs in Banking, IT, Quality control etc. They can even take up Actuarial Science as a specialization and join in various financial and share trading companies. Candidates with good flair and knowledge in Statistics are in huge demand in the present scenario.
Some of the leading Colleges that offer B.Sc. Statistics Degrees also offer placement services and can submit an application for jobs after their graduation. A student with Masters or Ph.D. in Statistics can apply for jobs such as a business analyst, statistics lecturer, professor etc. They can also go for jobs like software engineer, investigative officer, statistics analyst, researcher etc.

First of all, congratulations for your diploma. Now, coming to your question, one can only join any college for Bachelor's in the first year after his/her 12th through entrance examination or in merit basis. And in 2nd year, through lateral entry. No college offer direct admission in 3rd year of engineering. I have never heard so. You should keep yourself away from these types of myths. You should focus on your subjects and appear in graduate aptitude test in engineering (GATE) which is a national level engineering entrance examination. On the basis of graduate aptitude test in engineering marks, you can take admission in various reputed colleges of India for Masters Course. You can prepare for CAT to take admission in MBA colleges. I will suggest you not to change college. Dropping a year for better college may be a good choice. You may take a year drop and appear in lateral entry examination conducted by various colleges. If you want to complete your B.Tech from a centrally funded college, then I will suggest you to join Hemvati Nandan Bahuguna Garhwal University. Fee per semester is very less there (11000 per sem.) Rest is your choice.