Q: Suppose a data set has a mean of $$\bar{X} = 50$$ and a standard deviation of $$s = 5. $$What is the coefficient of variation (CV) for this data set?

$$CV = \frac{5}{50} \times 100\% = 10\%$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a fixed, unknown numerical value describing a characteristic of a population, while a statistic is a numerical value describing a characteristic of a sample.

Question 2

A researcher wants to study the average GPA of all students at a university. She selects 5 departments, then surveys every student in those departments. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which of the following variables is measured at the ratio level of measurement?

Accepted Answer

Weight of newborn babies in kilograms

Question 4

A sample consists of the following data: 2, 4, 4, 6, 8. What is the sample mean $$\bar{X}$$?

Accepted Answer

$$\bar{X} = \frac{2 + 4 + 4 + 6 + 8}{5} = 4.8$$

Question 5

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

Accepted Answer

It is sensitive to outliers.

Question 6

Given the sorted data set: 3, 5, 7, 8, 10, 12, 15, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 12 - 5 = 7$$

Question 7

A histogram of exam scores is bell-shaped and symmetric. According to the Empirical Rule, approximately what percentage of students scored within two standard deviations of the mean?

Accepted Answer

About 95%

Question 8

A data set has a mean of $$\bar{X} = 20$$ and a standard deviation of $$s = 4. $$What is the z-score for a value $$x = 28$$?

Accepted Answer

$$z = \frac{28 - 20}{4} = 2$$

Question 9

Which of the following best describes a convenience sample?

Accepted Answer

A sample formed from population elements which are readily available.

Question 10

A boxplot is constructed for a data set. Which of the following values is NOT part of the 5-number summary?

Accepted Answer

Sample mean

Question 11

A researcher collects data on the number of hours students study per week and their exam scores. Which type of graph is most appropriate to display the relationship between these two variables?

Accepted Answer

Scatter plot

Question 12

Suppose a data set has a mean of $$\bar{X} = 50$$ and a standard deviation of $$s = 5. $$What is the coefficient of variation (CV) for this data set?

Accepted Answer

$$CV = \frac{5}{50} 	imes 100\% = 10\%$$

Question 13

In a study, researchers want to determine if a new medication reduces blood pressure. They randomly assign participants to receive either the medication or a placebo and measure their blood pressure after 8 weeks. What type of study is this?

Accepted Answer

Experimental study

Question 14

A data set has a minimum value of 10, Q1 = 15, median = 20, Q3 = 25, and maximum value of 40. Which value would be considered an outlier?

Accepted Answer

A value of 40

Question 15

Which of the following best describes a systematic sampling method?

Accepted Answer

Selecting every kth element from a list after a random start

Question 16

A frequency table for test scores has class intervals of 50-59, 60-69, 70-79, and 80-89. What is the class width?

Accepted Answer

10

Question 17

If a data set is skewed right, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 18

According to Chebyshev’s Theorem, what is the minimum proportion of data values that must lie within $$K = 3$$ standard deviations of the mean for any data set?

Accepted Answer

$$1 - \frac{1}{3^2$} = 1 - \frac{1}{9} = \frac{8}{9}$$

Question 19

A time series plot is most appropriate for which of the following scenarios?

Accepted Answer

Displaying monthly sales revenue over several years

Question 20

A sample of 10 students has the following test scores: 60, 62, 65, 68, 70, 72, 75, 78, 80, 100. What is the range of the data?

Accepted Answer

$$100 - 60 = 40$$

STAT 241 Principles of Statistics: Data Collection and Summarization

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