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

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

Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$20$$

Question 3

Which measure of center is most affected by extreme values (outliers)?

Accepted Answer

Mean

Question 4

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

Accepted Answer

$$7$$

Question 5

Which of the following is a resistant measure of center?

Accepted Answer

Median

Question 6

Calculate the midrange for the following commute times (in minutes): 18, 22, 30, 35, 40.

Accepted Answer

$$\frac{18 + 40}{2} = 29$$

Question 7

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

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

Question 8

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 9

Given the following frequency distribution, estimate the mean:
Class Midpoints: 10, 20, 30
Frequencies: 2, 3, 5

Accepted Answer

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

Question 10

A data set has values: 8, 12, 15, 20, 25, 30. What is the median?

Accepted Answer

$$\frac{15 + 20}{2} = 17.5$$

Question 11

Which of the following statements about the mode is TRUE?

Accepted Answer

A data set can have more than one mode.

Question 12

If a data set consists of the values 2, 4, 6, 8, 100, which measure of center would best represent the 'typical' value?

Accepted Answer

Median

Question 13

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

Accepted Answer

It is resistant to outliers.

Question 14

A data set has the following values: 10, 20, 30, 40, 50. What is the midrange?

Accepted Answer

$$\frac{10 + 50}{2} = 30$$

Question 15

Which of the following is the correct formula for the sample mean $$\bar{x}$$?

Accepted Answer

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

Question 16

Why is the midrange rarely used in practice?

Accepted Answer

It is very sensitive to extreme values.

Question 17

Which of the following is an example of a bimodal data set?

Accepted Answer

Data set: 1, 2, 2, 3, 3, 4

Describing, Exploring, and Comparing Data: Measures of Center

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