Which of the following best describes the difference between a $\mathrm{population}$ and a $\mathrm{sample}$ in statistics?

• A. A $\mathrm{sample}$ includes all possible outcomes, while a $\mathrm{population}$ only includes observed outcomes.
• B. A $\mathrm{population}$ is always smaller than a $\mathrm{sample}$.
• C. A $\mathrm{population}$ includes all members of a defined group, while a $\mathrm{sample}$ is a subset of that group selected for analysis.
• D. A $\mathrm{sample}$ and a $\mathrm{population}$ are always the same in statistics.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the definition of a population in statistics. A population refers to the entire set of individuals, items, or data points that share a common characteristic and are the focus of a statistical study.
2. Step 2: Understand the definition of a sample. A sample is a subset of the population, selected to represent the population in a study, often because it is impractical or impossible to study the entire population.
3. Step 3: Compare the two concepts. The population includes all members of the defined group, while the sample includes only some members chosen from that group.
4. Step 4: Evaluate the given options based on these definitions. Identify which option correctly states that a population is the whole group and a sample is a part of that group.
5. Step 5: Conclude that the correct description is: 'A population includes all members of a defined group, while a sample is a subset of that group selected for analysis.'