Is there a "standard" method of breaking ties when rounding in the field of mathematics?

Question

I recently found that software packages deal with ties in different ways:

• round ties away from zero: round(0.5) = 1.0, round(1.5) = 2.0
• round ties to even: round(0.5) = 0.0, round(1.5) = 2.0

I am aware there other methods as well.

I am now looking for an authoritave source that supports one of these methods as being "standard" in mathematics. I found serveral online sources (1, 2, 3) that support the "away from zero" method as the "standard" but they don't seem to carry much authority.