Q: A frequency distribution for test scores is given. The midpoints of the classes are 55, 65, 75, and 85, with corresponding frequencies 2, 5, 8, and 5. What is the approximate mean score?

$$\frac{(55 \times 2) + (65 \times 5) + (75 \times 8) + (85 \times 5)}{2 + 5 + 8 + 5}$$

Q: A student receives the following grades in courses with different credit hours: A (4 credits), B (3 credits), C (2 credits), and F (1 credit). Using the quality points A=4, B=3, C=2, F=0, what is the student’s grade-point average (GPA)?

$$\frac{(4 \times 4) + (3 \times 3) + (2 \times 2) + (0 \times 1)}{4 + 3 + 2 + 1}$$

Question 1

A real estate analyst is comparing the sale prices of homes in a city. The data set contains several extremely high-priced luxury homes. Which measure of center is most appropriate to report the typical home price, and why?

Accepted Answer

The median, because it is resistant to outliers and better represents the center in skewed distributions.

Question 2

Given the following data set representing the number of books read by students in a month: 2, 3, 3, 5, 7, 8, 10, what is the median?

Accepted Answer

$$5$$

Question 3

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean uses every data value in its calculation.

Question 4

A student’s exam scores are 60, 70, 80, and 200. Which measure of center is LEAST affected by the outlier (200)?

Accepted Answer

Median

Question 5

A data set has the following values: 4, 8, 8, 10, 15. What is the mode?

Accepted Answer

$$8$$

Question 6

Which formula correctly represents the sample mean $$\bar{x}$$ for a set of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum x}{n}$$

Question 7

A frequency distribution for test scores is given. The midpoints of the classes are 55, 65, 75, and 85, with corresponding frequencies 2, 5, 8, and 5. What is the approximate mean score?

Accepted Answer

$$\frac{(55 	imes 2) + (65 	imes 5) + (75 	imes 8) + (85 	imes 5)}{2 + 5 + 8 + 5}$$

Question 8

A student receives the following grades in courses with different credit hours: A (4 credits), B (3 credits), C (2 credits), and F (1 credit). Using the quality points A=4, B=3, C=2, F=0, what is the student’s grade-point average (GPA)?

Accepted Answer

$$\frac{(4 	imes 4) + (3 	imes 3) + (2 	imes 2) + (0 	imes 1)}{4 + 3 + 2 + 1}$$

Question 9

Which of the following is NOT a property of the median?

Accepted Answer

The median is always equal to the mean in a skewed distribution.

Question 10

A data set consists of the following values: 12, 15, 18, 21, 24. What is the midrange?

Accepted Answer

$$\frac{12 + 24}{2} = 18$$

Question 11

In which scenario would the mode be the most appropriate measure of center?

Accepted Answer

When analyzing the most common shoe size sold in a store.

Question 12

A data set is left-skewed. Which of the following correctly describes the relative positions of the mean and median?

Accepted Answer

Mean \u003c Median

Question 13

Which of the following is a correct statement about the use of the term 'average' in statistics?

Accepted Answer

The term 'average' is not used by statisticians in professional journals.

Question 14

A data set contains the following values: 5, 7, 7, 8, 10, 12, 12, 12, 15. What is the mode?

Accepted Answer

$$12$$

Question 15

A student takes four exams and scores 88, 75, 95, and 100. Which measure of center is the student most likely to report to highlight their performance?

Accepted Answer

Mean

Question 16

Which of the following is the correct formula for the weighted mean $$\bar{x}$$ when data values $$x_1$$, $$x_2$$, ..., x_n$$ have corresponding weights w_1$, w_2$, ..., w_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum w x}{\sum w}$$

Question 17

Which of the following is a disadvantage of using the midrange as a measure of center?

Accepted Answer

It is highly sensitive to outliers.

Question 18

A data set has values: 2, 4, 6, 8, 10. If the largest value (10) is changed to 100, which measure of center will change the most?

Accepted Answer

Mean

Question 19

Which of the following is TRUE about the mode?

Accepted Answer

A data set can have more than one mode.

Question 20

A hospital administrator wants to summarize the most common blood type among patients. Which measure of center should be used?

Accepted Answer

Mode

Measures of Center in Statistics: Mean, Median, and Mode

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