Q: A student receives grades of A (4 credits), B (3 credits), C (2 credits), and F (1 credit). If the quality points are A=4, B=3, C=2, F=0, what is the weighted mean (GPA)?

$$\frac{4 \times 4 + 3 \times 3 + 2 \times 2 + 0 \times 1}{4 + 3 + 2 + 1} = \frac{16 + 9 + 4 + 0}{10} = \frac{29}{10} = 2.9$$

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 is NOT a property of the mean as a measure of center?

Accepted Answer

The mean can be substantially changed by a single extreme value.

Question 2

Given the data set: 12, 15, 18, 21, 24, what is the median?

Accepted Answer

$$18$$

Question 3

A data set contains the following values: 5, 7, 7, 9, 10, 10, 10, 12. What is the mode?

Accepted Answer

$$10$$

Question 4

Which formula correctly calculates the mean of a sample?

Accepted Answer

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

Question 5

Why is the midrange rarely used in practice?

Accepted Answer

It uses only the maximum and minimum values, making it very sensitive to extremes.

Question 6

A student receives grades of A (4 credits), B (3 credits), C (2 credits), and F (1 credit). If the quality points are A=4, B=3, C=2, F=0, what is the weighted mean (GPA)?

Accepted Answer

$$\frac{4 	imes 4 + 3 	imes 3 + 2 	imes 2 + 0 	imes 1}{4 + 3 + 2 + 1} = \frac{16 + 9 + 4 + 0}{10} = \frac{29}{10} = 2.9$$

Question 7

Which of the following situations is an example where calculating the mean or median is NOT meaningful?

Accepted Answer

Zip codes of famous landmarks.

Question 8

Given the data set: 8, 12, 15, 20, 22, what is the midrange?

Accepted Answer

$$\frac{8+22}{2} = 15$$

Question 9

If a data set has two values that occur with the same greatest frequency, what is the correct term for its mode?

Accepted Answer

Bimodal

Question 10

Which measure of center is most appropriate to use when a data set contains extreme outliers?

Accepted Answer

Median

Question 11

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 12

Which of the following is true about the mode?

Accepted Answer

It can be found for qualitative data.

Question 13

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

Accepted Answer

By computing the mean of the two middle numbers in the sorted list.

Question 14

Which of the following is a correct round-off rule for measures of center?

Accepted Answer

For the mean, median, and midrange, carry one more decimal place than is present in the original set of values.

Question 15

Which notation is used for the mean of a population?

Accepted Answer

$$\mu$$

Question 16

A data set contains the values: 3, 7, 7, 9, 12. What is the mean?

Accepted Answer

$$\frac{3+7+7+9+12}{5} = \frac{38}{5} = 7.6$$

Question 17

Which of the following is NOT a situation where the mean or median is meaningful?

Accepted Answer

Annual compensation of all employees in a company.

Question 18

Which measure of center is most likely to be confused with the median if not clearly defined?

Accepted Answer

Midrange

Question 19

If a data set has no repeated values, what is true about its mode?

Accepted Answer

There is no mode.

Measures of Center: Describing, Exploring, and Comparing Data

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