🧠 Suppose you are asked to estimate the average household income in Delhi. Which sampling method would you use and why?

🧠 Suppose you are asked to estimate the average household income in Delhi. Which sampling method would you use and why?

Answer: To estimate average household income in Delhi, the best design would be Stratified Multistage Sampling.

Step-by-Step Explanation:

1. Stratification: Delhi’s population is heterogeneous — it varies by region (North, South, East, West, Central), income level, and urban density.Therefore, we divide it into strata based on region or socioeconomic category.This ensures all types of households (slum, middle-class, high-income) are represented.

2. Multistage Approach:

   • Stage 1: Select wards or blocks (primary sampling units) from each region using Probability Proportional to Size (PPS) method.

   • Stage 2: Within each selected block, list all households and select a random sample using Simple Random Sampling Without Replacement (SRSWOR).

3. Estimator for Mean Income:

   
   

4. Variance of Estimate:

   
   

Why this method?

• Ensures representation from rich and poor localities.

• Controls variability due to heterogeneous income distribution.

• Cost-effective compared with complete enumeration.

  
  

Cross-Question: 👉 Why not use Simple Random Sampling?

Because it may over-represent easily accessible regions and under-represent high-income or remote clusters, leading to biased estimates.

ISS Practical Example:NSSO/NSO surveys on household consumption expenditure in Delhi follow this multistage-stratified design for accuracy and cost efficiency.