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

$$\frac{4 \times 3 + 3 \times 4 + 2 \times 2 + 1 \times 3 + 0 \times 1}{3+4+2+3+1} = \frac{12+12+4+3+0}{13} = \frac{31}{13} \approx 2.38$$

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

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

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, 18, 21, 24, what is the median?

Accepted Answer

$$18$$

Question 3

Which measure of center is most affected by an outlier in the data set?

Accepted Answer

Mean

Question 4

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

Accepted Answer

$$\frac{4 	imes 3 + 3 	imes 4 + 2 	imes 2 + 1 	imes 3 + 0 	imes 1}{3+4+2+3+1} = \frac{12+12+4+3+0}{13} = \frac{31}{13} \approx 2.38$$

Question 5

Which of the following is NOT a resistant measure of center?

Accepted Answer

Mean

Question 6

If a data set has values: 10, 20, 30, 40, 50, what is the midrange?

Accepted Answer

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

Question 7

Which scenario below illustrates when the mean and median are NOT meaningful statistics?

Accepted Answer

The zip codes of five famous landmarks.

Question 8

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

Accepted Answer

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

Question 9

Which of the following is true about the mode?

Accepted Answer

It can be used for qualitative data.

Question 10

A data set has values: 5, 7, 7, 8, 10, 10, 10, 12. What is the mode?

Accepted Answer

$$10$$

Question 11

Why is the midrange rarely used in practice?

Accepted Answer

It is very sensitive to extreme values.

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

There is no mode.

Question 14

Which of the following is a property of the median?

Accepted Answer

It is not affected by extreme values.

Question 15

A data set has values: 2, 4, 6, 8, 10, 12. What is the median?

Accepted Answer

$$7$$

Question 16

Which of the following best describes a resistant statistic?

Accepted Answer

A statistic that does not change much when extreme values are added.

Question 17

In a bimodal data set, which of the following is true?

Accepted Answer

There are two values that occur with the same greatest frequency.

Question 18

Which of the following is a correct step in calculating the median for an even number of data values?

Accepted Answer

Compute the mean of the two middle values.

Question 19

A hospital records the following patient ages: 22, 25, 25, 30, 35, 40, 40, 40, 45. What is the mode?

Accepted Answer

$$40$$

Question 20

Which of the following is a reason why the mean of the mean ages of each state does NOT represent the mean age of the entire United States?

Accepted Answer

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

Chapter 3: Describing, Exploring, and Comparing Data – Measures of Center

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