Lucas had all of the baseball fans at the school take a survey on school sports. Is this sample representative of the entire student body?

To determine whether Lucas's sample of baseball fans is representative of the entire student body, we need to consider a few important factors regarding sampling methods and representation.

1. Sample Composition: Firstly, if Lucas is only surveying baseball fans, this group may not accurately reflect the views of students involved in other sports or those who have no interest in sports at all. To be representative, a sample should include a diverse cross-section of the entire population.

2. Diversity of Opinions: The opinions of baseball fans could differ significantly from those of fans of other sports or from students who do not follow any sports. If the majority of the student body supports different sports, the results from this survey might be biased.

3. Size of the Sample: Additionally, the size of the sample matters. A larger, more diverse sample generally provides a better approximation of the views of the entire population compared to a small, homogeneous group.

4. Randomness: If Lucas’s sampling method was not random, this would further skew the results, as it might over-represent certain views while under-representing others.

In summary, unless Lucas included a wide range of students in the survey and ensured that it was conducted fairly and randomly, the sample of baseball fans is likely not representative of the entire student body. This limitation could lead to results that do not accurately reflect the opinions or preferences of all students.