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

$$\frac{(4 \times 3) + (3 \times 4) + (2 \times 3)}{3 + 4 + 3} = \frac{12 + 12 + 6}{10} = 3.0$$

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

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

Question 1

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

Accepted Answer

The sum of all data values divided by the number of data values.

Question 2

A data set contains the values: 10, 12, 15, 18, 100. Which measure of center is most affected by the outlier 100?

Accepted Answer

Mean

Question 3

Given the following data set: 8, 12, 15, 20, 25, what is the midrange?

Accepted Answer

$$\frac{8 + 25}{2} = 16.5$$

Question 4

Which of the following is a resistant measure of center?

Accepted Answer

Median

Question 5

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

Accepted Answer

$$\frac{(4 	imes 3) + (3 	imes 4) + (2 	imes 3)}{3 + 4 + 3} = \frac{12 + 12 + 6}{10} = 3.0$$

Question 6

Which of the following scenarios is it NOT appropriate to calculate the mean?

Accepted Answer

Zip codes of various landmarks.

Question 7

Given the data set: 5, 7, 7, 8, 10, 12, 12, 12, 15, what is the mode?

Accepted Answer

12

Question 8

If a data set has the values: 2, 4, 6, 8, 10, 12, what is the median?

Accepted Answer

$$\frac{6 + 8}{2} = 7$$

Question 9

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean uses every data value in its calculation.

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

It is affected by extreme values.

Question 12

A data set has values: 3, 7, 7, 9, 12, 15. What is the median?

Accepted Answer

$$\frac{7 + 9}{2} = 8$$

Question 13

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 14

Why is the midrange rarely used in practice?

Accepted Answer

It is very sensitive to extreme values.

Question 15

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

Accepted Answer

Numbers on football jerseys.

Question 16

If a data set has no repeated values, what can be said about the mode?

Accepted Answer

There is no mode.

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

$$\frac{2 + 4 + 6 + 8 + 10}{5} = 6$$

Describing, Exploring, and Comparing Data: Measures of Center

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