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Systematic sampling is a method where you select subjects at regular intervals from an ordered list. For instance, every 10th person in a line might be selected, as illustrated by the college cafeteria example in the exercise. This method is advantageous because it's straightforward and ensures that the sample is spread over the population.

However, there are important considerations to ensure the sample is not biased. If there's a pattern that matches the selection interval, this method can lead to a biased sample. For instance, if students with a certain major have class at the same time and thus eat at the same time every day, and your sampling interval coincides with this break period, you will overrepresent this group. To improve this method, it's vital that the starting point of the sampling is random, and the interval does not align with any pattern within the population.

A representative sample accurately reflects the characteristics of the population from which it's drawn. Achieving this is key for the validity of research findings.

In the scenario of the vacant lot, if only the Saturday afternoon resident's opinions are considered, the sample might not be representative. People who are at home on a Saturday afternoon could differ significantly from those who are not – perhaps they're more likely to be homeowners, older, or have children. To obtain a representative sample, you could randomly select different times and days to approach residents, or use different sampling methods such as phone or mail surveys that could reach a broader demographic, including those not reachable during a Saturday afternoon door-to-door visit.

Sampling biases occur when certain members or groups within the population are systematically more likely to be selected in the sample than others, or when the sampling method inherently leads to an unrepresentative sample.

Examples of such biases are present in both scenarios from the exercise. In the door-to-door petition scenario, people not at home during the collection time suffer from selection bias as they have no chance to participate. In the systematic sampling cafeteria scenario, students who don't eat there, who eat at non-peak times, or who are not on campus that day are also systematically excluded. Overcoming these biases often involves using multiple sampling methods and ensuring that every member of the population has an equal chance of being included in the sample. Awareness and anticipation of potential biases are key to choosing the right sampling technique for collecting data that can accurately inform decisions and conclusions.