Q: A student’s final grade is calculated using the following weights: Tests (60%), Final Exam (25%), Homework (10%), Project (5%). If the student scores 90 on tests, 80 on the final, 100 on homework, and 70 on the project, what is the weighted mean?

$$\bar{x} = \frac{(90 \times 0.6) + (80 \times 0.25) + (100 \times 0.1) + (70 \times 0.05)}{1} = 88.5$$

Question 1

Which of the following best describes the purpose of descriptive statistics?

Accepted Answer

To describe and summarize the main features of a data set, including its center and spread.

Question 2

Given the following notations, which one represents the sum of a set of values?

Accepted Answer

$$\sum x$$

Question 3

A researcher selects 15 students from a university of 10,000 students to record their weekly study hours. What are the sample size and population size?

Accepted Answer

Sample size: 15; Population size: 10,000

Question 4

Which of the following is NOT a measure of center?

Accepted Answer

Variance

Question 5

Calculate the sample mean for the following data set: 12, 25, 38, 5, 20.

Accepted Answer

$$\bar{x} = \frac{12 + 25 + 38 + 5 + 20}{5} = 20$$

Question 6

Which formula is used to calculate the mean of grouped data?

Accepted Answer

$$\bar{x} = \frac{\sum (x \cdot f)}{\sum f}$$

Question 7

A student’s final grade is calculated using the following weights: Tests (60%), Final Exam (25%), Homework (10%), Project (5%). If the student scores 90 on tests, 80 on the final, 100 on homework, and 70 on the project, what is the weighted mean?

Accepted Answer

$$\bar{x} = \frac{(90 	imes 0.6) + (80 	imes 0.25) + (100 	imes 0.1) + (70 	imes 0.05)}{1} = 88.5$$

Question 8

Why is the mean considered a non-resistant measure of center?

Accepted Answer

Because it is affected by extreme values (outliers).

Question 9

Which measure of center is most appropriate for a data set with extreme outliers?

Accepted Answer

Median

Question 10

Given the data set: 101, 106, 109, 116, 118, 135, 568, which measure of center is more resistant to the outlier 568?

Accepted Answer

Median

Question 11

Which of the following statements is TRUE about the mode?

Accepted Answer

The mode is the only measure of center that can be used with categorical data.

Question 12

A data set contains the values: 3, 4, 5, 6, 3, 4, 5, 7, 3, 4, 5, 8. How would you describe the number of modes in this data set?

Accepted Answer

Multimodal

Question 13

Calculate the midrange for the data set: 31, 19, 78, 65, 95.

Accepted Answer

$$midrange = \frac{95 + 19}{2} = 57$$

Question 14

Which of the following is NOT a measure of spread?

Accepted Answer

Mode

Question 15

If a distribution is perfectly symmetric, which of the following is true?

Accepted Answer

The mean and median will be equal.

Question 16

Which formula would you use to find the weighted mean of a set of grades with different weights?

Accepted Answer

$$\bar{x} = \frac{\sum (x \cdot w)}{\sum w}$$

Question 17

Which measure of center is most appropriate for describing the center of a skewed distribution?

Accepted Answer

Median

Question 18

Which of the following best describes the midrange?

Accepted Answer

The value midway between the maximum and minimum data values.

Descriptive Statistics: Measures of Center and Spread

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