Q: Suppose you are given the following five-number summary for exam scores: Minimum = 45, Q1 = 64, Median = 75, Q3 = 84, Maximum = 99. What is the interquartile range (IQR)?

$$\text{IQR} = Q_3$ - Q_1$ = 84 - 64 = 20$$

Q: Given the data set: 45, 51, 56, 63, 64, 68, 70, 75, 75, 78, 80, 84, 84, 84, 88, 90, 92, 95, 99. What is the range?

$$\text{Range} = 99 - 45 = 54$$

Question 1

Which of the following best describes the difference between a sample and a population in statistics?

Accepted Answer

A sample is a subset of the population, used to make inferences about the population.

Question 2

A researcher wants to study the effect of a new drug on blood pressure. She randomly assigns patients to either receive the drug or a placebo and compares their blood pressure after treatment. What type of study is this?

Accepted Answer

Randomized comparative experiment

Question 3

Which of the following variables is discrete?

Accepted Answer

The number of cars sold at a dealership each day

Question 4

Suppose you are given the following five-number summary for exam scores: Minimum = 45, Q1 = 64, Median = 75, Q3 = 84, Maximum = 99. What is the interquartile range (IQR)?

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$ = 84 - 64 = 20$$

Question 5

Which measure of central tendency is most affected by outliers?

Accepted Answer

Mean

Question 6

A box and whisker plot is most useful for:

Accepted Answer

Visualizing the spread and identifying outliers in a dataset

Question 7

Given the data set: 45, 51, 56, 63, 64, 68, 70, 75, 75, 78, 80, 84, 84, 84, 88, 90, 92, 95, 99. What is the range?

Accepted Answer

$$	ext{Range} = 99 - 45 = 54$$

Question 8

Which type of graph is best suited for displaying the distribution of a single quantitative variable?

Accepted Answer

Histogram

Question 9

In a linear regression equation $$y = a + bx$$, what does the coefficient $$b$$ represent?

Accepted Answer

The slope, or the change in $$y$$ for a one-unit increase in $$x$$

Question 10

A scatterplot shows a strong positive linear relationship between hours studied and exam grades. Which of the following best describes the correlation coefficient?

Accepted Answer

$$r is $$close to $$1$$

Question 11

If a data set is strongly skewed to the right, which measure of central tendency is likely to be greater?

Accepted Answer

Mean

Question 12

Which of the following is NOT a potential source of bias in data collection?

Accepted Answer

Random sampling

Question 13

Suppose the standard deviation of exam scores is $$10. $$According to the Empirical Rule, approximately what percentage of scores fall within two standard deviations of the mean?

Accepted Answer

About $$95\%$$

Question 14

A researcher collects data on hours studied and grades, and finds the regression equation $$	ext{Grade} = 45 + 7 	imes 	ext{Hours}. $$What is the predicted grade for a student who studies 4 hours?

Accepted Answer

$$45 + 7 	imes 4 = 73$$

Question 15

Which of the following best describes a residual in linear regression?

Accepted Answer

The difference between the observed value and the predicted value

Question 16

Which measure of spread is least affected by outliers?

Accepted Answer

Interquartile Range (IQR)

Question 17

In an observational study, which of the following is true?

Accepted Answer

The researcher observes subjects without intervention

Question 18

Which of the following is a parameter, not a statistic?

Accepted Answer

The average income of all adults in a country

Question 19

A pie chart is most appropriate for displaying:

Accepted Answer

The proportions of categories in a categorical variable

Question 20

A data set has a mean of $$80$$ and a standard deviation of $$5. $$According to the Empirical Rule, what is the range of values that contains approximately $$68\% of $$the data?

Accepted Answer

$$80 \pm 5$$, or $$75 to$$ $$85$$

Introductory Statistics: Review of Chapters 1–4

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