Final answer:
The manager's method of data collection through tracking the frequency of floor tile replacements is categorized as observation. Additionally, cluster sampling is identified as the survey design used for interviewing employees from randomly selected departments.
Step-by-step explanation:
The situation described where a manager of a department store collects data on the frequency of tile replacements in front of each entrance pertains to a measure of foot traffic, which serves as a proxy for the popularity of each entrance. The measurement situation being utilized here is best categorized as observation. Observation, in this case, is the method of collecting data on the physical wear and tear of floor tiles to infer which entrances receive the most use.
Looking at the provided options for survey designs, the manager of a department store who selects four departments at random to conduct interviews is using a cluster sampling design. This is because the manager is taking all the employees from a selected cluster (i.e., the department) for the survey.