High School

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------------------------------------------------ If a sample of 89 students is taken from a population of 530 students, the population variance, [tex]$\sigma^2$[/tex], is the variance of how many students' heights?



A. 530

B. Both 89 and 530

C. Neither 89 nor 530

D. 89

Answer :

We are given a population of 530 students and we have a sample of 89 students drawn from this population. The population variance, denoted by $ \sigma^2 $, is a parameter that reflects the spread of the measurements (in this case, heights) of the entire population. By definition, the population variance accounts for every individual within the population.

Since the population consists of 530 students, the variance being discussed is that of the heights of all $530$ students. Therefore, the correct answer is:

$$\textbf{530}.$$

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