Distance/Correspondence

Yes, you can go ahead with statistics. If you are a working professional in the field related to statistics. M.Sc in statistics will give you an extra edge in the professional world. Statistics and its application with modern tools and technique is of high demand and used everywhere like - production, marketing, sales etc. Statistical analysis is an inevitable part to control and guide for the business growth.
So, I think you are rightly thinking of Statistics. As you are thinking for distance mode of study - you may think for a course titled 'Post Graduate Diploma in Applied Statistics' offered by IGNOU.
However, go ahead based on your best interest.

Master of Science in Statistics or M.Sc. Statistics is a 3-year postgraduate course, the minimum eligibility for admission to which is completion of B.A. (Honors)/ B.Sc. (Honors) in Statistics or Mathematics, or graduation in a related discipline from a recognised university.
M.Sc Statistics: Who should opt? Ideal candidates of the course should be able to:
Apply Mathematics and Statistics to help develop solutions to practical problem.
Follow complex mathematical and statistical arguments and develop brief arguments of their own.
Operate mathematical and statistical computer software packages.
Find, extract, and analyze data from varied sources.
Communicate mathematical and statistical information effectively to generate feasible results.
Demonstrate sufficient organizational skills.
Eligibility for M.Sc. Statistics:
Candidates aspiring to pursue M.Sc. Statistics need to fulfil the below-mentioned eligibility criterion.
Completion of B.A. (Honors)/ B.Sc. (Honors) in Statistics or Mathematics or graduation in a related discipline from a recognised institute
Mathematics and Statistics as main subjects at the level of graduation
Minimum aggregate score of 60% at the level of graduation
Hope this helps. Regards.