Question

the data set on the right represents the population.

which formula should be used to calculate the variance?

a teacher recorded all of his students grades on the final exam as:

62, 77, 78, 80, 82, 82, 83, 84, 85, 87, 89, 95

consider the formulas:

\\(a: s^2 = \frac{(x_1 - \bar{x})^2 + (x_2 - \bar{x})^2 + ... + (x_n - \bar{x})^2}{n-1}\\)

\\(b: s = \sqrt{\frac{(x_1 - \bar{x})^2 + (x_2 - \bar{x})^2 + ... + (x_n - \bar{x})^2}{n-1}}\\)

\\(c: \sigma^2 = \frac{(x_1 - \mu)^2 + (x_2 - \mu)^2 + ... + (x_n - \mu)^2}{n}\\)

\\(d: \sigma = \sqrt{\frac{(x_1 - \mu)^2 + (x_2 - \mu)^2 + ... + (x_n - \mu)^2}{n}}\\)

Explanation:

Identify the data type

Using the Sample vs Population knowledge point
The problem states that the data set represents "the population" because the teacher recorded "all of his students' grades on the final exam."

Select the variance formula

Using the Population Variance Calculation knowledge point

• Formula A represents the sample variance \(s^2\).
• Formula B represents the sample standard deviation \(s\).
• Formula C represents the population variance \(\sigma^2\).
• Formula D represents the population standard deviation \(\sigma\).

Since we need to calculate the variance for a population, the correct formula is C.

Answer:

Which formula should be used to calculate the variance? <blank>C</blank>