In the following cookbook example:

http://yt-project.org/doc/cookbook/simple_plots.html#profiles-with-variance-values

the variance along the profile is extracted:

variance
= prof.variance['gas', 'velocity_magnitude'].value

but is then labelled as the standard deviation when the plot is created:

plt
.loglog(radius, variance, label='Standard Deviation')

So, does "prof.variance" return the standard deviation and not the variance?  Or, is the plot mislabelled?  Should the plot instead be:

plt.loglog(radius, np.sqrt(variance), label='Standard Deviation')