Answer :
To solve the problem, we need to understand what sample variance is and how it applies to the situation described in the question.
1. Definitions and Context:
- The term "sample variance" refers to a measure of variability or spread found in a sample of data. In statistics, when we calculate the variance of a sample, we are specifically concerned with the variability of that subset of the population we have chosen to observe.
- In this question, we're dealing with a population of 510 employees and a sample consisting of 82 employees.
2. Understanding What Sample Variance Represents:
- The sample variance, denoted as [tex]\( s^2 \)[/tex], is calculated using only the data from the sample, which, in this case, is the group of 82 employees.
- It gives us information about how spread out the salaries are within just those 82 employees chosen, not the entire population of 510.
3. Application to the Question:
- The question asks us to determine which group the sample variance [tex]\( s^2 \)[/tex] corresponds to. Since [tex]\( s^2 \)[/tex] is derived from the sample data, it specifically reflects the spread or variability of salaries among the 82 employees in the sample.
- Therefore, it does not directly describe the variance of all 510 employees’ salaries, as that would require a calculation using the entire population, typically referred to as the population variance.
4. Conclusion:
- Given that sample variance is calculated from and represents only the sample data, the correct answer is that it is the variance of the 82 employees' salaries.
Therefore, the sample variance [tex]\( s^2 \)[/tex] is the variance of the salaries of the 82 employees in the sample. The answer is A. 82.
1. Definitions and Context:
- The term "sample variance" refers to a measure of variability or spread found in a sample of data. In statistics, when we calculate the variance of a sample, we are specifically concerned with the variability of that subset of the population we have chosen to observe.
- In this question, we're dealing with a population of 510 employees and a sample consisting of 82 employees.
2. Understanding What Sample Variance Represents:
- The sample variance, denoted as [tex]\( s^2 \)[/tex], is calculated using only the data from the sample, which, in this case, is the group of 82 employees.
- It gives us information about how spread out the salaries are within just those 82 employees chosen, not the entire population of 510.
3. Application to the Question:
- The question asks us to determine which group the sample variance [tex]\( s^2 \)[/tex] corresponds to. Since [tex]\( s^2 \)[/tex] is derived from the sample data, it specifically reflects the spread or variability of salaries among the 82 employees in the sample.
- Therefore, it does not directly describe the variance of all 510 employees’ salaries, as that would require a calculation using the entire population, typically referred to as the population variance.
4. Conclusion:
- Given that sample variance is calculated from and represents only the sample data, the correct answer is that it is the variance of the 82 employees' salaries.
Therefore, the sample variance [tex]\( s^2 \)[/tex] is the variance of the salaries of the 82 employees in the sample. The answer is A. 82.
