Q: A frequency distribution for commute times (in minutes) is given. The class midpoints are 10, 20, 30, 40, and the frequencies are 2, 3, 5, 4, respectively. What is the approximate mean commute time?

$$ \frac{2 \times 10 + 3 \times 20 + 5 \times 30 + 4 \times 40}{2 + 3 + 5 + 4} = \frac{20 + 60 + 150 + 160}{14} = \frac{390}{14} \approx 27.9 $$

Q: A student’s grades and course credits are as follows: A (3 credits), B (4 credits), C (2 credits), F (1 credit). If A=4, B=3, C=2, F=0, what is the student’s weighted mean (GPA)?

$$ \frac{3 \times 4 + 4 \times 3 + 2 \times 2 + 1 \times 0}{3 + 4 + 2 + 1} = \frac{12 + 12 + 4 + 0}{10} = \frac{28}{10} = 2.8 $$

Question 1

Which of the following is a correct definition of the mean (arithmetic mean) for a data set?

Accepted Answer

The measure of center found by adding all of the data values and dividing the total by the number of data values.

Question 2

Given the data set: 10, 15, 20, 25, 100, which measure of center is most affected by the outlier 100?

Accepted Answer

Mean

Question 3

Which of the following formulas correctly represents the mean of a sample?

Accepted Answer

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

Question 4

A data set contains the values: 8, 12, 15, 20, 22. What is the median?

Accepted Answer

15

Question 5

Which of the following statements about the median is TRUE?

Accepted Answer

The median is a resistant measure of center.

Question 6

A set of exam scores is: 70, 80, 80, 90, 100. What is the mode?

Accepted Answer

80

Question 7

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

Accepted Answer

It is resistant to outliers.

Question 8

Given the data set: 5, 7, 9, 11, 13, 15. What is the midrange?

Accepted Answer

$$ \frac{15 + 5}{2} = 10 $$

Question 9

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

Accepted Answer

The zip codes of five famous landmarks.

Question 10

A frequency distribution for commute times (in minutes) is given. The class midpoints are 10, 20, 30, 40, and the frequencies are 2, 3, 5, 4, respectively. What is the approximate mean commute time?

Accepted Answer

$$ \frac{2 	imes 10 + 3 	imes 20 + 5 	imes 30 + 4 	imes 40}{2 + 3 + 5 + 4} = \frac{20 + 60 + 150 + 160}{14} = \frac{390}{14} \approx 27.9 $$

Question 11

A student’s grades and course credits are as follows: A (3 credits), B (4 credits), C (2 credits), F (1 credit). If A=4, B=3, C=2, F=0, what is the student’s weighted mean (GPA)?

Accepted Answer

$$ \frac{3 	imes 4 + 4 	imes 3 + 2 	imes 2 + 1 	imes 0}{3 + 4 + 2 + 1} = \frac{12 + 12 + 4 + 0}{10} = \frac{28}{10} = 2.8 $$

Question 12

Which of the following best describes a bimodal data set?

Accepted Answer

A data set with two values that occur with the same greatest frequency.

Question 13

Why is the midrange rarely used in practice as a measure of center?

Accepted Answer

It is very sensitive to extreme values (not resistant).

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

4

Question 16

Which of the following is a scenario where the mean is a meaningful statistic?

Accepted Answer

The annual incomes of a group of employees.

Question 17

If a data set has an even number of values, how is the median calculated?

Accepted Answer

By taking the mean of the two middle values in the sorted list.

Question 18

Which of the following is a resistant measure of center?

Accepted Answer

Median

Question 19

A data set contains the values: 3, 7, 7, 7, 12, 15, 20. What is the mean?

Accepted Answer

$$ \frac{3 + 7 + 7 + 7 + 12 + 15 + 20}{7} = \frac{71}{7} = 10.14 $$

Measures of Center: Describing, Exploring, and Comparing Data

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