Finding the average mass and uncertainty?

First of all you have the wrong formula for any known iron oxide. I assume you want iron (III) or ferric oxide, Fe2O3. 0.277/12 gives an average mass of 23.1 mg +/- 0.1 mg. The amount of iron in this is found by multiplying this number by the ratio of atmoic masses of two iron atoms to one ferric oxide formula unit: 111.7/159.7 x 23.1 mg = 16.2 mg, the correct answer