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

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

Question 1

A sample of exam scores is: 72, 85, 90, 90, 95, 100. What is the mode of this data set?

Accepted Answer

$$90$$

Question 2

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean is affected by outliers in the data set.

Question 3

Given the data set: 10, 12, 14, 16, 18, what is the median?

Accepted Answer

$$14$$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

Mode

Question 6

A frequency distribution has class midpoints $$x$$ and frequencies $$f. $$The mean of the grouped data is calculated as:

Accepted Answer

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

Question 7

A data set has the following values: 5, 7, 8, 12, 50. Which measure of central tendency is LEAST affected by the outlier 50?

Accepted Answer

Median

Question 8

If a distribution is skewed right (positively skewed), which of the following is true?

Accepted Answer

The mean is greater than the median.

Question 9

A hospital administrator wants to summarize the typical length of stay for patients. The data are highly skewed due to a few very long stays. Which measure should the administrator use?

Accepted Answer

Median

Question 10

Which of the following best describes a uniform distribution?

Accepted Answer

All classes have approximately equal frequencies.

Question 11

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

Accepted Answer

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

Question 12

Which of the following is NOT a property of the median?

Accepted Answer

It is affected by extreme values (outliers).

Question 13

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

Accepted Answer

$$\bar{x} = \frac{\sum x f}{\sum f}$$,\ where\ x\ is\ the\ class\ midpoint\ and\ f\ is\ the\ frequency

Question 14

In a data set with two modes, the distribution is called:

Accepted Answer

Bimodal

Question 15

A researcher collects the following data: 12, 15, 15, 18, 20, 22, 25. What is the median?

Accepted Answer

$$18$$

Question 16

Which of the following is the correct formula for the population mean?

Accepted Answer

$$\mu = \frac{\sum x}{N}$$

Question 17

A data set has the following values: 3, 3, 6, 7, 8, 9, 10. If the value 30 is added to the data set, which measure of central tendency will increase the most?

Accepted Answer

Mean

Question 18

Which of the following best describes a symmetric distribution?

Accepted Answer

The left and right halves of the distribution are mirror images.

Question 19

A data set has the following values: 1, 2, 2, 3, 4, 5, 6. What is the mode?

Accepted Answer

$$2$$

Question 20

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

Accepted Answer

The mean is less than the median.

Descriptive Statistics: Measures of Central Tendency

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