Now, if you're trying to figure out what Stats your Pokémon would have (as it is) at a different Level, here's how:

First, you need to take the effect of the Pokémon's Nature out of the equation.

Each Nature raises 1 Stat by 10%, and lowers 1 Stat by 10%, and 5 of them (Hardy, Docile, Serious, Bashful, and Quirky) raise the same Stat that they lower, with the result being no impact on Stats whatsoever.

It can sometimes be a bit difficult to reverse the effects of a Pokémon's Nature, due to how numbers are sometimes rounded up, and sometimes rounded down, but if you can get past that part (or if your Pokémon's Nature doesn't affect the Stat(s) you're trying to calculate), then the rest is a TON easier.

First, subtract your Pokémon's Stat by 5 (or if calculating HP, subtract by 10, and then subtract by your Pokémon's current Level), then divide it by your Pokémon's current Level.

Afterwords, to see what it's Stats would be at a different Level, simply multiply it by that Level, and then add 5 to it (or if calculating HP, add 10 instead, and then add HP equal to the Pokémon's Level to that).

It should be noted that while this technique works perfectly if you are using a Level 100 Pokémon, and trying to figure out what it's Stats would be at a lower Level (like 50), it may be slightly off when done on Pokémon of lower Levels, especially very low Level Pokémon.
(It can still be used to get an approximation, though.)

3 other techniques for figuring out Pokémon's Stats at different Levels are Mock Battles, the Battle Institute, and Rare Candies.

If you have a Battle Video you saved on your Vs. Recorder (as long as it's not a Multi Battle, Battle Royale, or any sort of Battle that has more than 2 people involved), you can do a Mock Battle with the Pokémon you're trying to calculate the Stats of, because it will have it's Level lowered to 50 (assuming it's higher than Level 50, anyway), and you can check it's Stats by looking at it's Summary during the Battle.
(This only works in Gens 6 & 7, however, as Mock Battles don't exist in older Games.)

The Battle Institute is also VERY useful for figuring out a Pokémon's Level 50 Stats, as it doesn't require you to save first, like other Battling Facilities, and is also one of the few places that will RAISE a Pokémon's Level to 50 if it's lower than that, as well as lower it if it's higher.
(If you have the Wii Game Pokémon Battle Revolution, you can use the "Level 50 All" Rules in the same way, as they also will raise or lower all Pokémons' Levels to 50.)

Rare Candies can be used to raise a Pokémon's Level VERY fast, so if you keep a bunch of them (like I do), then you can Save the Game, and then use them on your Pokémon to Level it up, so you can see what it's Stats will be at a higher Level, and then just soft reset afterwords.
(This technique can also be used to see what effect Evolving a Pokémon would have on it's Stats.)

Also, in all Pokémon Games (starting in Gen 4, I believe), there's some person called a Judge, who can evaluate your Pokémon's IVs, and tell you (roughly) how good it's Stats are overall, as well as which Stats it's best in, and how good it is in those.

This can be helpful for getting a rough idea of whether or not your Pokémon has good Stats or not, without having to do all of these calculations.

IMO, however, if you're catching a Legendary Pokémon, it's VERY important to make sure it has Great Stats, as well as the correct Nature, and so it'd probably be best to do use some of these techniques to see whether or not you got a good one.
(Because I'm such a perfectionist, I usually do this stuff with ALL of the Pokémon that I plan to use, lol!)

Anyway, I hope this Blog is helpful, and if anyone has any questions (including if you want me to try to calculate what effect something would have on a Pokémon's Stats for you), please leave a comment.

Sayonara!