Question:medium

Which of the following makes cluster sampling more efficient?

Show Hint

Cluster sampling works best when each cluster is a small-scale replica of the whole population, not a homogeneous group.
Updated On: Jul 4, 2026
  • By selecting clusters of small sizes
  • Choosing clusters having more variation among the units within a cluster
  • Choosing clusters having very less variation among the units within a cluster
  • By selecting clusters of large sizes
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Think of the variance decomposition for cluster sampling. The total population variance splits into a between-cluster component and a within-cluster component.
Step 2: The sampling variance of the cluster-sample mean depends mainly on the between-cluster variance, since only some clusters are chosen and each chosen cluster is studied completely. If clusters are internally heterogeneous (large within-cluster spread), the between-cluster means tend to be close to each other and close to the population mean, so between-cluster variance is small.
Step 3: A small between-cluster variance directly lowers the sampling error of the cluster-sample estimator, making the design more efficient. So clusters should deliberately be built so units differ a lot within each cluster.
This confirms that efficiency improves when there is $\text{high internal (within-cluster) variation}$.
\[\boxed{\text{More variation among units within a cluster}}\]
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