I am writing a finite element code for my final year project of BS Mechanical Engineering. The geometry is an integration of several parts composed of different materials. I don't have exact values of material properties. However, I do have ranges of them. For example, for Steel1020, Young's modulus varies from 205-215 GPa. Should I use lower limit of Young's modulus or higher limit of Young's modulus, or average (geometric / arithematic)?
As recommended by @Solar Mike, the most "professional" solution is to let the end-user decide. Give them some input mechanism (a textbox, slider or dropdown, for example) so they can define which value to adopt. This is what you'll see in basically any modeling software you'll find in the wild.
However, it's also very important to note the observations made in @alephzero's comment: it almost doesn't matter. The difference between 205 and 215 MPa is 4.5%. Given the errors involved in basically every step of an engineering design calculation*, that's peanuts.
Now, that being said, if you really want to take a strict approach to this, you need to look at the worst case. This will often be to simply adopt the lowest value. But not always.
And in this case, it might very well not be. If you are sandwiching different materials, one will be stronger than the other(s). In this case, you'll probably want to adopt the highest stiffness for the material with the lowest yield strength, and visa-versa.
This way, if these elements need to work together, the strong material will transfer the most force to the weaker material, increasing the likelihood that the weaker material yields first.
But then again, maybe the strong material would yield even earlier if it were stiffer (if it were right on the edge of yielding and the weaker material's increased stiffness is what's holding off the "straw that'd break the camel's back").
So this is a non-trivial question which depends on the specific case being analyzed. So, if you want to be strict about this, you'd either need to look at the specific case to determine the worst case or (if your program doesn't take ages to run) just run the model with the different combinations of moduli for each material and select the worst case.
* Every step of the process is an approximation: materials aren't perfectly elastic, they'll likely have different properties along a beam, supports and connections aren't perfectly fixed/pinned/springy, beam dimensions will be different, the welder will come to work drunk that day, etc.