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Here's an example of clusters in cluster analysis

In Cluster Analysis, clusters are usually "homogenous within" (that is, units within a cluster are close to each other ) and "heterogeneous within" (or clusters far from each other). In Survey Sampling, I've recently found out that clusters should be " as internally as heterogeneous as possible" (for example, a university as a cluster usually contains students, professors, workers, etc all very different from each other) and "as externally homogenous as possibile " (eg two universities usually have the same "structure" - with students, professors, workers, etc).

Which one is the correct reasoning behind a cluster structure ? Or, if the two are correct, why are the two reasonings different? As an example, what would happen if I performed cluster analysis on a population and then perform sampling on such "clustered" population? How should clusters be (internally/externally)?

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