JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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It is possible to delete only the submissions before 2016 in an easy way. Please on the submission area, select the settings icon > custom time frame > define start and end date (December 31st 2015):
Select delete submissions in time range:
Once deleted it is not possible to recover them, so please be sure before deleting them.
Let us know if we can assist you further.