Q: A student receives grades of A (4 points) in 3 credit hours, B (3 points) in 4 credit hours, and C (2 points) in 2 credit hours. What is the weighted mean (GPA)?

$$\displaystyle \frac{(4 \times 3) + (3 \times 4) + (2 \times 2)}{3 + 4 + 2} = \frac{12 + 12 + 4}{9} = \frac{28}{9} \approx 3.11$$

Q: A frequency distribution has the following 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 sample data: 12, 15, 18, 21, 24, what is the median?

Accepted Answer

$$\displaystyle 18$$

Question 3

A teacher records the following grades for a quiz: 7, 8, 8, 9, 10. What is the mode?

Accepted Answer

$$\displaystyle 8$$

Question 4

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 5

A student receives grades of A (4 points) in 3 credit hours, B (3 points) in 4 credit hours, and C (2 points) in 2 credit hours. What is the weighted mean (GPA)?

Accepted Answer

$$\displaystyle \frac{(4 	imes 3) + (3 	imes 4) + (2 	imes 2)}{3 + 4 + 2} = \frac{12 + 12 + 4}{9} = \frac{28}{9} \approx 3.11$$

Question 6

If a distribution is symmetric, which of the following is true?

Accepted Answer

The mean and median are equal.

Question 7

A frequency distribution has the following 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 8

Which of the following distributions is described as having a 'tail' that elongates more to the right?

Accepted Answer

Skewed right distribution

Question 9

In a negatively skewed (skewed left) distribution, how do the mean and median compare?

Accepted Answer

The mean is to the left of the median.

Question 10

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

Accepted Answer

$$\displaystyle \frac{5 + 7 + 7 + 8 + 10 + 12 + 15}{7} = \frac{64}{7} \approx 9.14$$

Question 11

Which measure of central tendency is most appropriate for categorical data, such as political party affiliation?

Accepted Answer

Mode

Question 12

A sample of ages in a class is: 20, 20, 20, 21, 21, 22, 22, 22, 65. Which measure best describes a typical age in this data set?

Accepted Answer

Median

Question 13

If a data set has two entries that occur with the same greatest frequency, what is the mode called?

Accepted Answer

Bimodal

Question 14

Which formula is used to estimate the mean of grouped data from a frequency distribution?

Accepted Answer

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

Question 15

A uniform distribution is best described as:

Accepted Answer

A distribution where all entries have equal or approximately equal frequencies.

Question 16

A hospital records the following patient weights (in kg): 60, 62, 65, 70, 120. Which measure of central tendency is least affected by the outlier?

Accepted Answer

Median

Question 17

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

Accepted Answer

Range

Question 18

A data set has the following values: 3, 5, 7, 9, 11, 13. What is the median?

Accepted Answer

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

Question 19

Which of the following statements is true about the mode?

Accepted Answer

A data set may have no mode if no value repeats.

Question 20

A researcher collects the following data: 2, 4, 4, 6, 8, 10. What is the mean?

Accepted Answer

$$\displaystyle \frac{2 + 4 + 4 + 6 + 8 + 10}{6} = \frac{34}{6} \approx 5.67$$

Descriptive Statistics: Measures of Central Tendency

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