I would like to know if someone with a BSc in Mathematics and Statistics can further study nursing or medical science.

Can anyone with experience help Eabioh with this?

You might have to make some enquiries to individual institutions to see what entry requirements are.

http://www.findamasters.com/

There are Nursing courses which can be done. They are short diploma courses which can be done by you. But you wont be able to do a bachelors or masters in Nursing or Medical Science. If you want Nursing as a profession you can opt for these courses. But it wont help you enter into a full fledged medical science career.