Experts in the subject are unhappy, fearing that key stage 4 is the wrong time to be introducing pupils to a "very sophisticated" topic that would be better left until A-level.
Standard deviation was a part of GCSE syllabuses until six years ago.
But it was then removed by the exams regulator, amid concerns from mathematicians that pupils were being taught to apply the function's formula without really understanding what it meant.
These fears have been revived, after the Qualifications and Curriculum Authority announced a recommendation to make it part of GCSEs for first teaching in 2010.
Consultation on the draft criteria has now closed. The QCA is due to publish final criteria in December.
Mathematics in Education and Industry (MEI), an independent curriculum development body, said in its response to the consultation: "Standard deviation was removed for good reasons. It was often taught incorrectly at this level."
Stella Dudzic, MEI's programme leader for the curriculum, said that teaching the subject at GCSE made sense when it was taught alongside related topics, such as the normal distribution. But, before its removal, it had been taught simply as a formula. "Students have been left with the impression that standard deviation is nothing more than a very complicated calculation," said the submission.