Conclusion: 

The analysis of the data revealed neither causation nor common response. Instead, it showed that there is no correlation, possibly due to the presence of many confounding or lurking variables. In our observational study, we only measured family size and average grades, but there may be other factors affect a students' marks in school, such as their socioeconomic background. Further, the number of siblings may not affect a student as much as the presence of siblings. For example, older or younger siblings that  score higher marks may or may not influence others' academic achievement. Supposing that they do have some influence, they can either encourage their siblings to perform better, or discourage them from working as hard. This also applies to siblings that score lower marks. Because each individual case is different, it is clear that no concrete correlation can be found, and thus, our hypothesis was incorrect. 

However, with less bias, our data might have show a stronger correlation. There was even more nonresponse than anticipated, but there was undercoverage in one important aspect. Only one of the surveyed students was an only child, with no siblings. Students without siblings would have yielded the most useful data because all or most of their family's resources have been allotted to them. However, because this group was so underrepresented, no reliable data can be compiled on this topic. 

Further, poorly worded questions may have thrown off the data. Though there were only two questions, many students asked for clarification on the first one. Though we specified that respondents should write down their weighted GPA, most were unsure which year's GPA to supply. Though we verbally specified to students the 10th through 12th grade weighted GPAs, it is likely that many put down their GPA for 9th through 12th grade, or just for the current semester. Additionally, some people may have been uncertain as to what their GPA was, and approximated an answer. This caused a lot of round-numbered responses, making the highest frequency of scores around 4.0. 

If this observational study was redone, the samples could have been improved with a SRS, stratified random sampling (from all grade levels), cluster sampling and multi-stage sampling. The design of the study was adequate, but more randomization and replication (at least sampling more groups of students) could have yielded better results. We had originally intended to analyze the number of sisters and number of brothers separately, and although that would be an interesting study, it would create three explanatory variables to work with. 

These results would, at best, represent the population of AP students in Southern California. Students who are not taking AP classes would not be able to report weighted grades, and students outside of Southern California may not score as high due to varying socioeconomic statuses.