Q: A student’s grades and credits are as follows: A (3 credits), B (4 credits), C (2 credits). If A=4, B=3, C=2, what is the weighted mean (GPA)?

$$\displaystyle \frac{(4 \times 3) + (3 \times 4) + (2 \times 2)}{3+4+2} = \frac{12+12+4}{9} = \frac{28}{9} \approx 3.11$$

Q: A frequency distribution has class midpoints 10, 20, 30 with frequencies 2, 3, 5 respectively. What is the approximate mean?

$$\displaystyle \frac{(10 \times 2) + (20 \times 3) + (30 \times 5)}{2+3+5} = \frac{20+60+150}{10} = \frac{230}{10} = 23$$

Q: If the mean commute time for a sample of 10 people is 25 minutes, what is the total sum of all commute times?

$$\displaystyle 25 \times 10 = 250$$

Question 1

Which of the following statements best describes the mean of a data set?

Accepted Answer

It is the sum of all data values divided by the number of data values.

Question 2

Given the data set: 12, 15, 20, 22, 25, what is the median?

Accepted Answer

$$\displaystyle 20$$

Question 3

A data set consists of the following values: 5, 7, 7, 8, 10. What is the mode?

Accepted Answer

$$\displaystyle 7$$

Question 4

Which measure of center is most affected by outliers?

Accepted Answer

Mean

Question 5

Calculate the midrange for the following data set: 3, 7, 10, 15, 20.

Accepted Answer

$$\displaystyle \frac{3+20}{2} = 11.5$$

Question 6

A student’s grades and credits are as follows: A (3 credits), B (4 credits), C (2 credits). If A=4, B=3, C=2, what is the weighted mean (GPA)?

Accepted Answer

$$\displaystyle \frac{(4 	imes 3) + (3 	imes 4) + (2 	imes 2)}{3+4+2} = \frac{12+12+4}{9} = \frac{28}{9} \approx 3.11$$

Question 7

Which of the following is a resistant measure of center?

Accepted Answer

Median

Question 8

A frequency distribution has class midpoints 10, 20, 30 with frequencies 2, 3, 5 respectively. What is the approximate mean?

Accepted Answer

$$\displaystyle \frac{(10 	imes 2) + (20 	imes 3) + (30 	imes 5)}{2+3+5} = \frac{20+60+150}{10} = \frac{230}{10} = 23$$

Question 9

Which of the following data sets is most likely to have no mode?

Accepted Answer

5, 7, 9, 11, 13

Question 10

Why is it inappropriate to calculate the mean of zip codes?

Accepted Answer

Zip codes are categorical labels and do not represent measurable quantities.

Question 11

If a data set has the values 10, 12, 14, 16, 18, 20, what is the median?

Accepted Answer

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

Question 12

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

Accepted Answer

It is resistant to outliers.

Question 13

A data set has values: 2, 4, 4, 6, 8, 8, 10. What is the mode?

Accepted Answer

4 and 8

Question 14

Which of the following best describes the midrange?

Accepted Answer

The value midway between the maximum and minimum values.

Question 15

A hospital administrator wants to summarize the ages of patients in the emergency room. Which measure of center is most appropriate if the data are highly skewed with several outliers?

Accepted Answer

Median

Question 16

If the mean commute time for a sample of 10 people is 25 minutes, what is the total sum of all commute times?

Accepted Answer

$$\displaystyle 25 	imes 10 = 250$$

Question 17

Which of the following is an example where the mean and median are not meaningful statistics?

Accepted Answer

Numbers on football jerseys

Question 18

A data set has values: 1, 2, 3, 4, 100. Which measure of center best represents the typical value?

Accepted Answer

Median

Question 19

If a data set is multimodal, which of the following is true?

Accepted Answer

There are more than two values that occur with the greatest frequency.

Question 20

A company’s top 5 CEO salaries are: $$500M, 300M$$, $$200M, 150M$$, $100M. Why is the mean not a good measure of center for this data?

Accepted Answer

The data are not representative of the larger population.

Describing, Exploring, and Comparing Data: Measures of Center

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