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Answer :
To solve this question, we need to understand the concept of sample variance. The sample variance, denoted as [tex]\( s^2 \)[/tex], is a statistical measure that describes the variability or spread of data points in a sample.
In the context of this question:
1. Population vs. Sample:
- Population: This refers to the entire group of items or people that you're interested in studying, in this case, all 510 employees.
- Sample: This is a subset of the population, selected for analysis, which in this question is 82 employees.
2. Sample Variance:
- The sample variance [tex]\( s^2 \)[/tex] is calculated from the sample data. It measures how much the salaries of the sample (82 employees) are spread out.
3. What the Question is Asking:
- The question is seeking to determine how many employees' salaries are represented by the sample variance [tex]\( s^2 \)[/tex].
Since the sample variance [tex]\( s^2 \)[/tex] is calculated using the salaries of the sample group (82 employees), it reflects the variability within this sample, not the entire population.
Therefore, the correct answer is:
A. 82
The sample variance reflects the variance of the sample of 82 employees.
In the context of this question:
1. Population vs. Sample:
- Population: This refers to the entire group of items or people that you're interested in studying, in this case, all 510 employees.
- Sample: This is a subset of the population, selected for analysis, which in this question is 82 employees.
2. Sample Variance:
- The sample variance [tex]\( s^2 \)[/tex] is calculated from the sample data. It measures how much the salaries of the sample (82 employees) are spread out.
3. What the Question is Asking:
- The question is seeking to determine how many employees' salaries are represented by the sample variance [tex]\( s^2 \)[/tex].
Since the sample variance [tex]\( s^2 \)[/tex] is calculated using the salaries of the sample group (82 employees), it reflects the variability within this sample, not the entire population.
Therefore, the correct answer is:
A. 82
The sample variance reflects the variance of the sample of 82 employees.
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