Summary of Conclusions

We found that our sample distribution matched fairly well with Poisson statistics. Furthermore, the Gaussian distribution of the data very quickly became a good fit to the data. Both experimental and statistical errors were apparent in our experiment as well. Experimental errors came from the equipment dropping counts in some cases. This could be somewhat minimized by limiting the range of our data to a few standard deviations from the mean to eliminate some of the more erroneous data. Even after doing this, however, there was still enough experimental error that could be seen from figure 3. Statistical errors, on the other hand, provided us ways to quantify the error in our data. By calculating and examining the standard deviations, we could analyze how the error changes as we vary different parameters of the experiment. In the end, we found that decreasing the rate or increasing the brightness of the LED created more experimental errors, but did not change the statistical errors very much. The Poisson and Gaussian were very good fits for all of our data sets. Increasing the number of samples for each data set, on the other hand did show a change in the error of our approximations. We found that as we increased the number of samples for each data set, the error that we can state for our mean would decrease by a factor of $\sqrt{N}$. Therefore, to increase the accuracy of our data by a factor of 2, we had to take 4 times the number of samples for each data set.