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Answer :
Sure, let's understand the question step by step:
The question is asking about the population variance, [tex]\(\sigma^2\)[/tex], and we need to determine how many students' heights this variance represents.
1. Population vs Sample:
- A population refers to the entire group that you want to draw conclusions about. Here, the population is 550 students.
- A sample is a subset of the population taken to make estimates or test hypotheses about the population. Here, the sample consists of 173 students.
2. Population Variance ([tex]\(\sigma^2\)[/tex]):
- The term "population variance" refers to a statistical measure that calculates the spread or dispersion of the entire population's values, in this case, the heights of the 550 students.
- It takes into account every individual in the population, which means all of the 550 students.
3. Given Options:
- A. 550: This option represents the variance for the entire population, which matches the definition of population variance.
- C. 173: This refers to the sample, but sample variance is denoted differently and does not represent the entire population.
- B and D can be disregarded because they do not correctly apply to the definition of population variance.
Therefore, the population variance, [tex]\(\sigma^2\)[/tex], indeed refers to the variance of the whole population, which is 550 students.
So, the correct answer is A. 550.
The question is asking about the population variance, [tex]\(\sigma^2\)[/tex], and we need to determine how many students' heights this variance represents.
1. Population vs Sample:
- A population refers to the entire group that you want to draw conclusions about. Here, the population is 550 students.
- A sample is a subset of the population taken to make estimates or test hypotheses about the population. Here, the sample consists of 173 students.
2. Population Variance ([tex]\(\sigma^2\)[/tex]):
- The term "population variance" refers to a statistical measure that calculates the spread or dispersion of the entire population's values, in this case, the heights of the 550 students.
- It takes into account every individual in the population, which means all of the 550 students.
3. Given Options:
- A. 550: This option represents the variance for the entire population, which matches the definition of population variance.
- C. 173: This refers to the sample, but sample variance is denoted differently and does not represent the entire population.
- B and D can be disregarded because they do not correctly apply to the definition of population variance.
Therefore, the population variance, [tex]\(\sigma^2\)[/tex], indeed refers to the variance of the whole population, which is 550 students.
So, the correct answer is A. 550.
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