Systematic random sampling involves selecting elements at:

Systematic random sampling is a method of sampling that involves selecting elements from an ordered list at regular intervals. This technique is effective because it allows for a straightforward approach to create a sample that is representative of the population.

In this method, one typically starts at a random point in the list and then selects every nth element. The 'n' value is determined based on the total population size and the desired sample size. For example, if you want a sample of 100 from a population of 1,000, you might select every 10th individual after choosing a random starting point. This regular interval ensures that the sample maintains a level of randomness while also being systematic, reducing bias that might arise from purely random selections.

Selecting at random intervals, as stated in another option, does not ensure the regularity that systematic random sampling requires. Similarly, simply picking arbitrary points or relying on a thorough analysis signifies a non-systematic approach that does not align with the clear and methodical nature of systematic random sampling.