The sample of patients selected by the doctor using a computer to make a list of every patient between the ages 18 and 25 and selecting every third name on this list may not be representative of the population of her patients.
This is because the selection process is not random and may introduce bias into the sample. By selecting every third name on the list, the doctor is using a systematic sampling method, which may inadvertently exclude certain types of patients from the sample. For example, if the list is sorted in some way, patients with certain characteristics may tend to appear more frequently or less frequently in the sample.
Furthermore, the age range of 18 to 25 may not be representative of the entire population of the doctor's patients. There may be other age groups that are underrepresented or overrepresented in the sample, which could affect the overall representativeness of the sample.
To obtain a representative sample, the selection process should be random and unbiased. This can be achieved by using a random sampling method, such as simple random sampling or stratified random sampling, where the sample is selected randomly from the entire population or from different subgroups of the population. This would help to ensure that all types of patients are equally likely to be included in the sample and that the sample is more likely to be representative of the population of the doctor's patients.