Q: A student received the following grades with corresponding credit hours: A (4 credits), B (3 credits), C (2 credits). If A=4, B=3, C=2, what is the weighted mean (GPA)?

$$\displaystyle \frac{4 \times 4 + 3 \times 3 + 2 \times 2}{4+3+2} = \frac{16+9+4}{9} = \frac{29}{9} \approx 3.22$$

Q: A frequency distribution has the following class midpoints and frequencies: Midpoints: 10, 20, 30; Frequencies: 2, 3, 5. What is the estimated mean?

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

Question 1

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

Accepted Answer

The 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 student received the following grades with corresponding credit hours: A (4 credits), B (3 credits), C (2 credits). If A=4, B=3, C=2, what is the weighted mean (GPA)?

Accepted Answer

$$\displaystyle \frac{4 	imes 4 + 3 	imes 3 + 2 	imes 2}{4+3+2} = \frac{16+9+4}{9} = \frac{29}{9} \approx 3.22$$

Question 4

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 5

A frequency distribution has the following class midpoints and frequencies: Midpoints: 10, 20, 30; Frequencies: 2, 3, 5. What is the estimated mean?

Accepted Answer

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

Question 6

In a data set with values: 5, 7, 7, 8, 10, 12, 15, which value is the mode?

Accepted Answer

$$\displaystyle 7$$

Question 7

A distribution of salaries in a company is highly skewed to the right. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 8

Which of the following best describes a uniform distribution?

Accepted Answer

All entries or classes have equal or approximately equal frequencies.

Question 9

If a data set has an even number of entries, how is the median calculated?

Accepted Answer

It is the mean of the two middle data entries.

Question 10

A hospital administrator wants to summarize the typical length of stay for patients. The data set contains a few extremely long stays due to rare complications. Which measure of central tendency should the administrator use to best represent a typical stay?

Accepted Answer

Median

Question 11

Which formula correctly represents the sample mean $$\bar{x}$$ for a data set with $$n$$ entries $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 12

A survey asks people to name their favorite fruit. Which measure of central tendency is most appropriate for summarizing the responses?

Accepted Answer

Mode

Question 13

A data set has the following values: 2, 4, 4, 6, 8, 10, 100. Which measure of central tendency is most influenced by the value 100?

Accepted Answer

Mean

Question 14

Which of the following statements is true for a symmetric distribution?

Accepted Answer

The mean, median, and mode are all equal.

Question 15

A teacher wants to estimate the mean test score from a grouped frequency distribution. Which formula should be used?

Accepted Answer

$$\displaystyle \bar{x} = \frac{\sum (x \cdot f)}{n}$$, where $$x is $$the class midpoint and $$f is $$the frequency

Question 16

In a left-skewed (negatively skewed) distribution, which of the following is true?

Accepted Answer

The mean is to the left of the median.

Question 17

A data set contains the following values: 10, 12, 14, 16, 18, 20. What is the mean?

Accepted Answer

$$\displaystyle 16$$

Question 18

Which of the following real-world scenarios would most likely result in a bimodal distribution?

Accepted Answer

Heights of adult men and women combined in a population.

Question 19

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

Accepted Answer

The data set has no mode.

Question 20

A researcher is analyzing the number of hours people spend on their phones per day. The data is grouped into intervals. What is the first step in estimating the mean from this grouped data?

Accepted Answer

Find the midpoint of each class interval.

Descriptive Statistics: Measures of Central Tendency

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