Variables Stars on the main sequence?Watch
E. G. Most astronomers would say the Sun is variable' and that's main sequence.
Variable is a catch-all term for stars that have been observed vary in apparent magnitude (as seen from earth)
That splits down into two categories
Intrinsic variables which are variable because the luminosity of the star varies
Extrinsic variables which are variable for some extraneous reason such as being in an eclipsing binary system or being having the light blocked by an accretion disk (or exoplanets)
The majority of stars are binaries but most of them won't be orbiting in a plane that'll make an eclipse visible to us
If you were able to wait long enough I suppose they'd all vary eventually.- the main sequence is a phase that stars pass through. A protostar varies in luminosity to get on to the main sequence and it'll inevitably vary again when it leaves the main sequence.
You'll probably only have to worry about variables that can be used as standard candles* and perhaps variability caused by an exoplanet being used as a method of discovering exoplanetary systems.
e.g. type Ia supernovae (cataclysmic variable is a subcategory of intrinsic)
Cepheids and RR Lyrae (periodic variables)
periodic variables similar to Cepheids (and RR Lyrae) only occur in a fairly small part of the Hertzsprung Russell diagram though...