Introduction:
Multi-stage sampling is a sampling technique that involves dividing the population into smaller subgroups or stages, and then selecting samples from each stage. This method is particularly useful when the population is large and heterogeneous.

Explanation:
1. Large and Heterogeneous Population:
Multi-stage sampling is most useful when dealing with large and heterogeneous populations. In such populations, there may be significant variations in characteristics, such as demographics, preferences, or behaviors. By dividing the population into smaller subgroups or stages, multi-stage sampling allows for a more efficient and representative selection of samples.

2. More Efficient Sampling:
Multi-stage sampling is more efficient than simple random sampling or other sampling methods when dealing with large populations. It reduces the time, cost, and effort required to collect data by selecting samples from smaller subgroups or stages instead of the entire population.

3. Representative Samples:
By selecting samples from each stage or subgroup, multi-stage sampling ensures that the samples are representative of the population as a whole. This is important when dealing with large and heterogeneous populations because it allows for the inclusion of different characteristics and variations within the samples.

4. Improved Precision:
Multi-stage sampling can also lead to improved precision in estimating population parameters. By selecting samples from each stage or subgroup, it allows for a more accurate estimation of population characteristics. This is especially beneficial when detailed prior information is not available or when a high level of accuracy is required.

Conclusion:
In conclusion, multi-stage sampling is particularly useful when dealing with large and heterogeneous populations. It allows for more efficient sampling, representative samples, and improved precision in estimating population parameters. This method can be applied in various research studies, surveys, and data collection processes to obtain reliable and valid results.