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

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

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, 100, which measure of central tendency best represents a typical value for this data set?

Accepted Answer

Median

Question 4

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

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

Accepted Answer

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

Question 6

A frequency distribution for daily screen time (in minutes) is grouped into classes. To estimate the mean screen time, which value should be used for each class in the calculation?

Accepted Answer

The midpoint of each class

Question 7

A data set has the following values: 5, 7, 8, 12, 15, 18, 20. What is the median?

Accepted Answer

$12$

Question 8

In a left-skewed (negatively skewed) distribution, which of the following is true about the relationship between the mean and the median?

Accepted Answer

The mean is less 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 patients with extremely long stays. Which measure of central tendency should be used?

Accepted Answer

Median

Question 10

Which of the following best describes a uniform distribution?

Accepted Answer

All entries or classes have equal or approximately equal frequencies.

Question 11

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

Accepted Answer

2 and 4

Question 12

Which of the following is a disadvantage of using the mean as a measure of central tendency?

Accepted Answer

It is greatly affected by outliers.

Question 13

A teacher wants to estimate the mean test score for a large class using grouped data. The frequency distribution is as follows: 60-69 (5 students), 70-79 (10 students), 80-89 (15 students), 90-99 (10 students). What is the formula to estimate the mean?

Accepted Answer

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

Question 14

Which of the following distributions is most likely to have the mean greater than the median?

Accepted Answer

Positively skewed (skewed right) distribution

Question 15

A data set consists of the following values: 10, 12, 14, 16, 18, 20. What is the median?

Accepted Answer

$15$

Question 16

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

Accepted Answer

Mode

Question 17

If a data set is symmetric, which of the following is true?

Accepted Answer

The mean and median are approximately equal.

Question 18

A class of 20 students has the following ages: 18 students are 20 years old, 1 student is 21, and 1 student is 65. Which measure of central tendency is most affected by the 65-year-old student?

Accepted Answer

Mean

Question 19

A data set has no repeated values. What can be said about the mode?

Accepted Answer

There is no mode.

Question 20

A researcher is analyzing the number of hours worked per week by employees at a company. The data are grouped into classes. Which steps are necessary to estimate the mean number of hours worked?

Accepted Answer

Find the midpoint of each class, multiply by the class frequency, sum the products, and divide by the total number of data values.

Measures of Central Tendency in Descriptive Statistics

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