Q: Which of the following is a correct formula for the midrange of a data set?

$$\text{Midrange} = \frac{\text{maximum data value} + \text{minimum data value}}{2}$$

Q: A student receives the following grades and credits: A (3 credits), B (4 credits), C (3 credits), D (2 credits). If A=4, B=3, C=2, D=1, what is the student's grade-point average (GPA)?

$$\frac{(3 \times 4) + (4 \times 3) + (3 \times 2) + (2 \times 1)}{3+4+3+2} = \frac{12+12+6+2}{12} = \frac{32}{12} = 2.67$$

Question 1

Which of the following statements best describes why the mean is not considered a resistant measure of center?

Accepted Answer

The mean can be substantially affected by extreme values (outliers).

Question 2

Given the following data set representing the number of hours five students studied for an exam: 2, 4, 6, 8, 100. Which measure of center would be most appropriate to describe the typical number of hours studied?

Accepted Answer

Median, because it is resistant to the extreme value.

Question 3

A researcher collects the jersey numbers of all players on a basketball team and calculates the mean. Why is this calculation not meaningful?

Accepted Answer

Jersey numbers are merely labels and do not measure or count anything.

Question 4

Calculate the mean of the following commute times (in minutes): 15, 20, 25, 30, 35.

Accepted Answer

$$\frac{15+20+25+30+35}{5} = 25$$

Question 5

A data set has the following values: 10, 12, 14, 16, 18, 20. What is the median?

Accepted Answer

$$\frac{14+16}{2} = 15$$

Question 6

Which of the following is a correct formula for the midrange of a data set?

Accepted Answer

$$	ext{Midrange} = \frac{	ext{maximum data value} + 	ext{minimum data value}}{2}$$

Question 7

A frequency distribution for commute times is given. The midpoint of each class is multiplied by its frequency, and the sum of these products is divided by the sum of the frequencies. What is this calculation an approximation of?

Accepted Answer

The mean from a frequency distribution

Question 8

A student receives the following grades and credits: A (3 credits), B (4 credits), C (3 credits), D (2 credits). If A=4, B=3, C=2, D=1, what is the student's grade-point average (GPA)?

Accepted Answer

$$\frac{(3 	imes 4) + (4 	imes 3) + (3 	imes 2) + (2 	imes 1)}{3+4+3+2} = \frac{12+12+6+2}{12} = \frac{32}{12} = 2.67$$

Question 9

Which of the following data sets is bimodal?

Accepted Answer

5, 5, 10, 10, 15

Question 10

Why is the mean of the top 5 CEO salaries in a country not a meaningful statistic for describing the typical CEO salary?

Accepted Answer

Because the top 5 salaries are not representative of the larger population of CEO salaries.

Question 11

Which of the following is true about the mode?

Accepted Answer

A data set can have no mode, one mode, or multiple modes.

Question 12

A data set consists of the following values: 3, 7, 7, 10, 12, 12, 15. What is the mode?

Accepted Answer

The data set is bimodal: 7 and 12.

Question 13

Which of the following is the correct formula for the weighted mean?

Accepted Answer

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

Question 14

Which of the following scenarios would make the median a better measure of center than the mean?

Accepted Answer

A data set with a strong outlier.

Question 15

If a data set consists of the values 2, 4, 6, 8, and 10, what is the midrange?

Accepted Answer

$$\frac{10+2}{2} = 6$$

Question 16

Which of the following is NOT a situation where calculating the mean or median is meaningful?

Accepted Answer

Calculating the mean of commute times in minutes.

Question 17

A data set contains the values: 5, 7, 9, 11, 13, 15, 17, 19. What is the median?

Accepted Answer

$$\frac{11+13}{2} = 12$$

Question 18

Which of the following best describes why the mean of the means of each state’s average age does not equal the mean age of the entire U.S. population?

Accepted Answer

Because the population sizes of the states are not taken into account.

Measures of Center: Describing, Exploring, and Comparing Data

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