Q: A student receives the following grades with corresponding credit hours: A (4 credits, 3 points), B (3 credits, 2 points), C (2 credits, 1 point). What is the weighted mean (GPA)?

$$\displaystyle \frac{4 \times 3 + 3 \times 2 + 2 \times 1}{4 + 3 + 2} = \frac{12 + 6 + 2}{9} = \frac{20}{9} \approx 2.22$$

Q: A frequency distribution for screen time (in minutes) is given. The midpoints are 100, 200, 300, 400 with frequencies 2, 5, 8, 5. What is the estimated mean screen time?

$$\displaystyle \frac{2 \times 100 + 5 \times 200 + 8 \times 300 + 5 \times 400}{2 + 5 + 8 + 5} = \frac{200 + 1000 + 2400 + 2000}{20} = \frac{5600}{20} = 280$$

Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$\displaystyle 18$$

Question 3

A data set contains the values: 5, 7, 7, 8, 10, 12, 12, 12, 15. What is the mode?

Accepted Answer

$$\displaystyle 12$$

Question 4

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 5

A student receives the following grades with corresponding credit hours: A (4 credits, 3 points), B (3 credits, 2 points), C (2 credits, 1 point). What is the weighted mean (GPA)?

Accepted Answer

$$\displaystyle \frac{4 	imes 3 + 3 	imes 2 + 2 	imes 1}{4 + 3 + 2} = \frac{12 + 6 + 2}{9} = \frac{20}{9} \approx 2.22$$

Question 6

Which of the following distributions is both symmetric and unimodal?

Accepted Answer

Normal distribution

Question 7

A frequency distribution for screen time (in minutes) is given. The midpoints are 100, 200, 300, 400 with frequencies 2, 5, 8, 5. What is the estimated mean screen time?

Accepted Answer

$$\displaystyle \frac{2 	imes 100 + 5 	imes 200 + 8 	imes 300 + 5 	imes 400}{2 + 5 + 8 + 5} = \frac{200 + 1000 + 2400 + 2000}{20} = \frac{5600}{20} = 280$$

Question 8

Which measure of central tendency should be used when the data are skewed or contain outliers?

Accepted Answer

Median

Question 9

A distribution of salaries in a company is highly skewed to the right due to a few very high executive salaries. Which measure best represents a typical employee's salary?

Accepted Answer

Median

Question 10

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

Accepted Answer

$$\displaystyle 6$$

Question 11

Which of the following statements is true about the mode?

Accepted Answer

A data set can have more than one mode.

Question 12

A distribution is described as uniform. Which of the following is true?

Accepted Answer

All entries have equal or approximately equal frequencies.

Question 13

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 14

A sample of exam scores is: 70, 75, 80, 85, 90, 95, 100. If the score 100 is replaced by 200, which measure will change the most?

Accepted Answer

Mean

Question 15

Which formula is used to estimate the mean of grouped data?

Accepted Answer

$$\displaystyle \bar{x} = \frac{\sum (x \cdot f)}{\sum f}$$

Question 16

Which of the following best describes a symmetric distribution?

Accepted Answer

A vertical line can be drawn through the middle and the halves are mirror images.

Question 17

In a normal distribution, which of the following is true?

Accepted Answer

The mean, median, and mode are all equal.

Question 18

A data set has the following values: 10, 12, 14, 16, 18, 100. Which measure of central tendency is least affected by the outlier 100?

Accepted Answer

Median

Question 19

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

Accepted Answer

Data set with two values occurring with the same highest frequency.

Question 20

A researcher collects the following data on political party affiliation: Democrat, Republican, Democrat, Independent, Democrat, Republican. What is the mode?

Accepted Answer

Democrat

Descriptive Statistics: Measures of Central Tendency

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