What is the best method to collect data on the average ages of math and science teachers?

Using a census to collect data on the average ages of math and science teachers is the most comprehensive approach, as it aims to gather information from every individual within the specified population rather than a subset. When conducting a census, you eliminate sampling error because you are including the entire group of math and science teachers in your research.

This method ensures that the data collected is accurate and reflects the true average age, as every teacher's age will be accounted for without the influence of sampling variability. A census provides a complete picture and is particularly effective when the population is manageable in size.

In contrast, a random sample could lead to variability in the ages reported, as the results would depend on the specific sample chosen, which may not capture the overall age distribution accurately. Surveys rely on voluntary responses, which may introduce bias or non-response issues, leading to incomplete data. Observation would not be a suitable method for directly measuring ages, as it would not provide the specific information needed for this analysis.