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If a sample of 26 students is taken from a population of 135 students, the population variance, [tex]\sigma^2[/tex], is the variance of how many students' heights?

A. Neither 26 nor 135
B. 26
C. 135
D. Both 26 and 135

Answer :

To solve the problem, we need to understand the difference between a population variance and a sample variance.

1. Population Variance ([tex]$\sigma^2$[/tex]):
- Population variance is a measure of how data points in an entire population are spread out. In this case, the population consists of all 135 students. Thus, the population variance is calculated using the data for all 135 students.

2. Sample Variance:
- Sample variance, on the other hand, is estimated from a sample to reflect how data points are spread out within that sample. In this case, a sample of 26 students is taken from the population of 135 students.

The question asks us to identify the number of students for which the population variance ([tex]$\sigma^2$[/tex]) is defined. Since the population variance is based on the whole population, it corresponds to the number of students in the population, which is 135.

Therefore, the population variance, [tex]$\sigma^2$[/tex], is the variance of the whole population of 135 students.

So the correct answer is:
C. 135

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