Cluster Sampling

The population is divided into clusters, each of which represents a mini-population. A random sample of clusters is selected, and all elements within chosen clusters are observed.

Mathematical Idea

Let:
  • Population divided into \( K \) clusters
  • Select \( k \) clusters randomly
Then the estimator of the population mean is:
$$ \bar{Y} = \frac{1}{k} \sum_{i=1}^{k} \bar{Y}_i $$

where \( \bar{Y}_i \) is the mean of cluster \( i \).

Key Difference from Stratified Sampling

  • Stratified sampling: sample from every group
  • Cluster sampling: sample entire groups