[grimkc]

I noticed that the definition of atomic mass is the average mass of all the isotopes of an element; hence the atomic mass is a decimal number. My question is does an atom with no specified isotope exist in nature or are the elements in periodic table just average element atoms?

[Enthalpy]

Hi Grimkc, welcome here!

All atoms have an integer number of protons and neutrons. The decimal number for the mass comes from:

• the mean value between several isotopes as you pointed out;
• and also the energy emitted when the protons and neutrons combined, making the nucleus lighter.

A few elements have only one natural isotope, for instance Be, Co, Th. You can check that their mass isn't an integer neither.
http://www.webelements.com/cobalt/isotopes.html