Young's Modulus Calculations

I understand that we are using the deflections to calculate the Young's Modulus, but with so many data points, should we get a value for each test of each length and then calculate the avg and the error? Or would we just choose a random point length and weight to calculate it from there?

When trying to calculate the Young's modulus, I was expecting to get a value for each set of mass and length combinations that were approximately the same since the modulus depends on load, length, and strain so they should theoretically each affect each other and come out to the same modulus for the material. However, I noticed that, for example 5 Inch 150 gram 8 Inch 150 gram and 11 Inch 150 gram static tests, the mean strain values were roughly the same. Thus, my modulus is changing relative to the differing loads and lengths but not being compensated by a change in the strain, so the modulus varies widely across tests. Am I not correct in assuming that the mean strain across these 3 lengths independent of load should increase as the length goes up? If this is the case, how should we go about justifying that our data that we recorded is not in accord...?

You could potentially just use your load measurements at one length for the elastic modulus. Remember, you are ultimately going to want to plot stress versus strain and use the slope to calculate the elastic modulus. Strain, you physically measured using the strain gauge. The stress at the strain gauge is what you need to calculate...think about what length is relevant for this calculation and that should clear up the confusion.