Frances, although the Scots officially changed to the Gregorian "new style" calendar in 1752 along with the rest of Britain following Chesterfield's Act, Scotland had already changed the start of their year to 1st January in 1600.
(The Gregorian calendar had been adopted on the Continent in 1582.)

In the rest of Britain by 1751 the Julian calendar was 11 days out of step, and the Act stated that 1st January should be the first day of the year, which previously had been 25th March. So 1751 commenced March 25th and ended Dec 31st 1751.1752 commenced 1st Jan. and ended 31st Dec 1752 after omitting 11 days in September to bring it into line with the Gregorian calendar.

In the IOM it was rather erratic with some registers using the old style for some entries after 1751.
However it can easily be seen on the register or filmed copy, but much harder on an index, e.g. the IGI where they seemed to ignore the actual year (as we know it now) but wrote only what was written on the register even though it was clearly, for example, 1754/55.

Sue