Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain.
The average GPA of the 85 students on a college football team roster

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Step 1: Understand the problem. The goal is to determine whether to take a census (collect data from all 85 students) or use a sampling (collect data from a subset of the 85 students). A census is typically used when the population size is small and manageable, while sampling is used for larger populations or when time/resources are limited.

Step 2: Evaluate the population size. In this case, the population consists of 85 students, which is relatively small. Conducting a census might be feasible since it would involve collecting data from all 85 students.

Step 3: Consider the resources and time available. If collecting data from all 85 students is practical and does not require excessive time or resources, a census might be the best choice. However, if there are constraints, sampling could be a better option.

Step 4: If sampling is chosen, determine the appropriate sampling technique. Common techniques include: (a) Simple Random Sampling: Each student has an equal chance of being selected. (b) Stratified Sampling: Divide the team into subgroups (e.g., by position) and sample from each subgroup. (c) Systematic Sampling: Select every k-th student from a list. (d) Convenience Sampling: Choose students who are easiest to access. (e) Cluster Sampling: Divide the team into clusters (e.g., offense and defense) and sample entire clusters.

Step 5: Justify the choice of sampling technique. For example, if the goal is to ensure representation across different positions on the team, stratified sampling might be appropriate. If simplicity is the priority, simple random sampling could be used. Clearly explain why the chosen method is suitable for the context.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Census vs. Sampling

A census involves collecting data from every member of a population, providing complete and accurate information. In contrast, sampling involves selecting a subset of the population to estimate characteristics of the whole. Sampling is often more practical and cost-effective, especially when dealing with large populations, such as a college football team roster.

Sampling Techniques

Sampling techniques are methods used to select individuals from a population for data collection. Common techniques include random sampling, where each member has an equal chance of selection, and stratified sampling, which involves dividing the population into subgroups and sampling from each. The choice of technique affects the representativeness and reliability of the results.

Average GPA Calculation

The average GPA is calculated by summing the GPAs of all students and dividing by the total number of students. This measure provides a central tendency of academic performance within the group. Understanding how to calculate and interpret the average GPA is essential for evaluating the academic standing of the football team and making informed decisions based on the data.

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