I did a back titration with an unknown carbonate and using the average % carbonate (by mass) which I found to be 27.40% and appropriate calculation decided where the unknown is an alkali metal carbonate or an alkaline earth metal carbonate. I have no idea how to tell the difference between to two using the percentage.

I think it would be Mg but I am still unsure as to what calculations to use

I'm not sure from your description exactly what you've done; however, one way you can check it is to calculate % carbonate in the few alkali and alkaline earth metal carbonates.

Li2CO3 - = (60/73.9)*100 = 81.2
Na2CO3= (60/106)* 100 = 56.6
K2CO3 = (60/138.3)*100 = 43.4%
MgCO3 is (60/84.3)*100 = 71.1
CaCO3 = (60/100)^100 = 60%
You aren't likely to have Rb2CO3 or Cs2CO3 but Rb2CO3 is (60/230.9)*100 = 26%
MgCO3 isn't soluble in water. Was your sample soluble in water? How much confidence to you have in the 27.4.

It was in HCl, the 27.4% was obtained through the lab

To determine whether the unknown carbonate is an alkali metal carbonate or an alkaline earth metal carbonate, you can use the average % carbonate (by mass) and the appropriate calculation.

Here's how you can differentiate between the two types of carbonates using the percentage:

1. Alkali Metal Carbonates:
Alkali metal carbonates include compounds such as sodium carbonate (Na2CO3), potassium carbonate (K2CO3), and lithium carbonate (Li2CO3).
These carbonates have a higher percentage of carbonate than alkaline earth metal carbonates. In general, alkali metal carbonates have percentages greater than 30%.

2. Alkaline Earth Metal Carbonates:
Alkaline earth metal carbonates include compounds such as calcium carbonate (CaCO3), magnesium carbonate (MgCO3), and strontium carbonate (SrCO3).
These carbonates have a lower percentage of carbonate compared to alkali metal carbonates. In general, alkaline earth metal carbonates have percentages below 30%.

Based on the given information, since the average % carbonate (by mass) is 27.40%, it falls within the range of alkaline earth metal carbonates. Therefore, the unknown carbonate is most likely an alkaline earth metal carbonate.

Please note that this is a general guideline, and other factors such as experimental error or impurities can affect the accuracy of the determination. It's always recommended to perform additional tests or confirmatory experiments to validate the identification of the unknown carbonate.