gjv,
You should take off the barrel and slug it from the breach end toward the muzzle end. Most airgun barrels have choke(an area of tighter constriction thought to aid with accuracy with pellets) on the muzzle end. This choke usually has an adverse affect on accuracy of slugs(as slugs don't require any choke in the barrel to be accurate).
Push one slug thru until it starts to get tight near the muzzle end at the choke. Then stop and push it back out toward the breach and measure it. You will need calipers that measure to at least the thousanths(.001) of an inch. This will give you the diameter of your BORE. Then push another slug thru all the way out the muzzle end and measure it. This will give you the diameter of the CHOKE(good to know how much constriction the choke is putting on your slug). You want to size your slug .001 larger the measurement of the BORE(part of the barrel which extends from the breach to near the muzzle end of the barrel), not the CHOKE(last few inches of the barrel where the final constriction is). If you size the slug to the CHOKE, then the slug will be too small in the breach/bore part of the barrel and you will get "blow-by" as air escapes around the slug, being too small to seal the gap. I don't know how tight the choke is on your (Avenger)barrel, but it will be a tighter constriction than the bore. If it is a MUCH tighter diameter than the bore, you may not find a size of slug that is super accurate. I doubt that is the case as many people shoot slugs out of Avengers(I would have thought one of them might have already responded to your question with what works well in their guns by now).
I know this is a lot, but it's good info to have the process to finding the right size slug for your gun. All else is trial and error. But, I would advise you to ALWAYS trust YOUR results out of YOUR gun over anything anyone tells you should happen(everyone's individual situation is unique to them). I have learned from the many people on the forum know a lot more than me. Perhaps some of them with specific experience with the Avenger barrel can help.
Good luck