Q: If a data set has a mean $$\mu = 50$$ and a standard deviation $$\sigma = 5$$, according to the Range Rule of Thumb, what value would be considered significantly high?

$$\mu + 2\sigma = 50 + 2 \times 5 = 60 or $$higher

Q: A student’s percentile rank on a test is calculated using the formula $$P = \frac{\#\ below\ x}{n} \times 100\%. If 18 $$students scored below a student in a class of 25, what is the student’s percentile rank?

$$P = \frac{18}{25} \times 100\% = 72\%$$

Question 1

Which of the following best describes a parameter in statistics?

Accepted Answer

A numerical summary describing a characteristic of a population.

Question 2

A researcher wants to study the average cholesterol level of adults in a city. She randomly selects 200 adults from the city and records their cholesterol levels. What is the population in this scenario?

Accepted Answer

All adults in the city.

Question 3

Which of the following is an example of a convenience sample?

Accepted Answer

A professor surveys students leaving her own class to estimate the average study time of all university students.

Question 4

Which of the following best distinguishes an experiment from an observational study?

Accepted Answer

In an experiment, researchers actively impose treatments on subjects.

Question 5

A data set contains the following values: 2, 4, 4, 5, 7. What is the mode?

Accepted Answer

4

Question 6

Which measure of center is most resistant to outliers?

Accepted Answer

Median

Question 7

A distribution is right-skewed. Which of the following is most likely true?

Accepted Answer

Mean \u003e Median \u003e Mode

Question 8

Given the data set: 3, 7, 7, 10, 12, what is the range?

Accepted Answer

$$12 - 3 = 9$$

Question 9

If a data set has a mean $$\mu = 50$$ and a standard deviation $$\sigma = 5$$, according to the Range Rule of Thumb, what value would be considered significantly high?

Accepted Answer

$$\mu + 2\sigma = 50 + 2 	imes 5 = 60 or $$higher

Question 10

Which of the following statements about the Empirical Rule is correct?

Accepted Answer

Approximately 68% of data falls within one standard deviation of the mean in a bell-shaped distribution.

Question 11

A student scores 85 on a test with a mean of 75 and a standard deviation of 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 12

Which of the following is a property of the standard deviation?

Accepted Answer

It is always non-negative.

Question 13

Which type of graph is most appropriate for displaying the distribution of a categorical variable such as favorite color?

Accepted Answer

Bar chart

Question 14

A boxplot is constructed for a data set. Which of the following statements is true?

Accepted Answer

The box represents the interquartile range (IQR), and the line inside the box is the median.

Question 15

If a value is more than 1.5 IQRs above the third quartile (Q3), what is it considered?

Accepted Answer

An outlier

Question 16

Which of the following best describes a voluntary response sample?

Accepted Answer

A sample in which participants choose to be included, often leading to bias.

Question 17

A frequency table for test scores has class limits 60-69, 70-79, 80-89, and 90-99. What is the class width?

Accepted Answer

$$70 - 60 = 10$$

Question 18

Which of the following is a key difference between Chebyshev’s Theorem and the Empirical Rule?

Accepted Answer

Chebyshev’s Theorem applies to all distributions, while the Empirical Rule applies only to bell-shaped distributions.

Question 19

A student’s percentile rank on a test is calculated using the formula $$P = \frac{\#\ below\ x}{n} 	imes 100\%. If 18 $$students scored below a student in a class of 25, what is the student’s percentile rank?

Accepted Answer

$$P = \frac{18}{25} 	imes 100\% = 72\%$$

Question 20

A hospital administrator wants to estimate the average length of stay for patients. She collects data from every patient admitted in the past year. What type of data collection is this?

Accepted Answer

Census

STAT 243Z Exam 1 Review: Foundations of Statistics

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