Previous UPSC Statistics Optional exams have featured a range of case studies that test candidates' understanding of statistical concepts and their ability to apply them to real-world scenarios. Here are a few examples:

1. Case Study: Population Growth
This case study may involve analyzing population growth trends in a particular country or region. Candidates may be provided with historical data on population size, birth rates, death rates, and migration patterns. They would then be required to analyze and interpret the data to identify key trends, calculate growth rates, and make projections for the future.

2. Case Study: Market Research
In this case study, candidates may be presented with market research data related to a specific product or industry. They would need to analyze the data to identify consumer preferences, market trends, and potential target segments. Candidates may also be asked to develop a statistical model to forecast demand or assess the impact of certain factors on the market.

3. Case Study: Quality Control
This case study may focus on quality control procedures in a manufacturing or service industry. Candidates may be given data on product defects, customer complaints, or process variables. They would need to apply statistical techniques such as hypothesis testing, control charts, or regression analysis to evaluate the quality of the product or process and suggest improvements.

4. Case Study: Financial Analysis
Candidates may be presented with financial data of a company or industry and asked to analyze its performance. They may need to calculate financial ratios, perform trend analysis, or assess the impact of certain factors on profitability. Candidates may also be required to make recommendations based on the analysis, such as investment decisions or cost-cutting measures.

5. Case Study: Epidemiology
This case study may involve analyzing data related to the spread of a disease or public health issue. Candidates may be given information on the number of cases, mortality rates, risk factors, or intervention strategies. They would need to apply statistical methods such as incidence rates, odds ratios, or survival analysis to assess the impact of the disease and evaluate the effectiveness of interventions.

These case studies not only test candidates' knowledge of statistical techniques but also their ability to interpret and communicate the results effectively. By analyzing real-world scenarios, candidates can demonstrate their understanding of statistical concepts and their application in various fields.