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Answer :
Sure, let's go through the question step-by-step.
The question is asking about the interpretation of the population variance, denoted as [tex]\(\sigma^2\)[/tex], in the context of a sample and a population.
1. Understanding Population Variance ([tex]\(\sigma^2\)[/tex]):
Population variance is a measure of how data points in a full population are spread out. It represents the average of the squared differences from the mean for every individual in the population.
2. Population vs. Sample:
- Population: This is the entire group that you are interested in studying. In this case, it is the 135 students.
- Sample: This is a subset of the population that is selected for study. Here, it is the 26 students taken from the population of 135 students.
3. Context of the Question:
- The question asks about the variance of how many students' heights is represented by the population variance ([tex]\(\sigma^2\)[/tex]).
- Population variance describes the variability of the entire population's heights, which here is the 135 students, not just those in a sample.
4. Conclusion:
Since [tex]\(\sigma^2\)[/tex] represents the variance within the entire population, it pertains to the 135 students.
Therefore, the correct answer is B. 135 because the population variance is a characteristic of the entire population of 135 students.
The question is asking about the interpretation of the population variance, denoted as [tex]\(\sigma^2\)[/tex], in the context of a sample and a population.
1. Understanding Population Variance ([tex]\(\sigma^2\)[/tex]):
Population variance is a measure of how data points in a full population are spread out. It represents the average of the squared differences from the mean for every individual in the population.
2. Population vs. Sample:
- Population: This is the entire group that you are interested in studying. In this case, it is the 135 students.
- Sample: This is a subset of the population that is selected for study. Here, it is the 26 students taken from the population of 135 students.
3. Context of the Question:
- The question asks about the variance of how many students' heights is represented by the population variance ([tex]\(\sigma^2\)[/tex]).
- Population variance describes the variability of the entire population's heights, which here is the 135 students, not just those in a sample.
4. Conclusion:
Since [tex]\(\sigma^2\)[/tex] represents the variance within the entire population, it pertains to the 135 students.
Therefore, the correct answer is B. 135 because the population variance is a characteristic of the entire population of 135 students.
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