Mendeleev created this table as he noticed that a metal that was reactive with water always seemed to
come before a metal that was also very reactive and
then a less reactive metal, noticing a pattern in
chemical properties. But what group of atoms did he
totally leave out? Why do you think that is?

Mendeleev had left the noble gases out of his periodic table.

Explanation:

Mendeleev's periodic table is pictured in the image attached to the question.

Mendeleev's table obviously lacked the noble gases. The reason for this grave omission is simple; the noble gases were not known as at the time when he formulated his periodic table. There weren't any known elements  whose properties were similar to the  properties of the noble gases. This would have lead him to suspect their existence.

your picture is not part of the scientific method.