A motion request sample without replacement, also known as sampling without replacement, is a statistical technique used to select a subset of data without returning the selected items back to the original population. This means that once an item is selected, it is removed from the population and cannot be selected again. This method is used to ensure that each selected item is unique and to prevent any bias in the sampling process. Sampling without replacement is commonly used in various research methodologies, including market research, social sciences, and data analysis. It helps to obtain a representative sample that accurately reflects the characteristics of the population being studied. By not replacing the selected items, the sample maintains the same distribution and variability as the original population, making it suitable for making inferences and drawing conclusions. There are different types of motion request samples without replacement that can be employed depending on the research objectives and requirements: 1. Simple Random Sampling without Replacement: This method involves selecting items randomly from the population without any specific criteria or stratification. It ensures that every possible combination of items has an equal chance of being selected, minimizing sampling biases. 2. Stratified Sampling without Replacement: In this technique, the population is divided into distinct strata or subgroups based on certain characteristics or variables. Then, samples are selected from each stratum using a random sampling method without replacement. This approach ensures that the sample represents each stratum proportionally, making it suitable for studying specific subgroups within the population. 3. Cluster Sampling without Replacement: Cluster sampling involves dividing the population into clusters or groups based on geographical boundaries or other identifiable units. In this method, a sample of clusters is randomly selected, and all items within the selected clusters are included in the sample without replacement. Cluster sampling without replacement helps reduce costs and time in data collection, especially when the clusters are already geographically close. 4. Systematic Sampling without Replacement: Systematic sampling involves selecting every nth item from the population after initially selecting a random starting point. This method ensures an equal probability of selection for each item in the population. Systematic sampling without replacement is efficient and easy to implement when the population is organized in a particular order or sequence. In conclusion, a motion request sample without replacement is a statistical approach used to select unique subsets of data without returning the selected items back to the original population. It helps in obtaining representative samples and minimizing biases in various research areas. Different types of sampling without replacement exist, including simple random sampling, stratified sampling, cluster sampling, and systematic sampling, each offering distinct advantages depending on the research objectives.