WHIRLWIND EXPLANATION: Pokémon have a fixed, permanent score from 0 to 31 for each stat that affects how good that stat can ever get.

This calculator will figure out that score (called a "gene" or, more obtusely, an "IV") for you, so you can discard the unworthy. It's more accurate for higher-level Pokémon, so it's helpful to go into a level 100 wifi battle with someone and check your Pokémon's stats from there.

Stat calculator

Charizard
Charizard 		Base
stats		 Stats Effort Stats Effort Possible genes (IVs)
Level Level
HP 78
214–239
impossible
Attack 84
139–164
impossible
Defense 78
129–154
impossible
Special Attack 109
179–204
impossible
Special Defense 85
141–165
impossible
Speed 100
165–189
impossible

Uh-oh. The set of stats you gave is totally impossible. Better double-check against your game.

The most common problem is effort; if a Pokémon has been trained at all, it'll have some effort accumulated. This affects its stats, and there's no way to know how much effort it has unless you've been keeping track. Sorry.

If you're desperate, you could try the effort-lowering berries (Pomeg et al.), which will reduce effort in a given stat by 10 at a time. Drop every stat's effort until it won't drop any further, then try again.

or start over