New issue 1308: profile variance vs standard deviation https://bitbucket.org/yt_analysis/yt/issues/1308/profile-variance-vs-standar...
yt/data_objects/profiles.py :: _finalize_storage()
all_var = np.sqrt(all_var)
which later is used to construct "self.variance". So, after this line, both "all_var" and the public-facing member "variance" is really a standard deviation.
The cookbook example "profile_with_variance.py" correctly labels prof.variance as "standard deviation" in the generated plot.
The consensus arising from the mailing list discussion (http://lists.spacepope.org/pipermail/yt-users-spacepope.org/2017-January/008...) was that public facing members of profile instances should be correctly named and the cookbook example should be adjusted to follow whatever convention is chosen.
Perhaps add a profile.standard_deviation member and throw a deprivation warning on profile.variance ... ?