Question 1

Which of the following is a resistant measure of center when describing a quantitative variable?

Accepted Answer

The median

Question 2

Given a dataset with a strong right skew (such as the total number of Olympic medals per country), which measure of center is most appropriate to report?

Accepted Answer

The median, because it is resistant to outliers

Question 3

Which of the following is the correct formula for the Z-score of an observation $$x$$ from a dataset with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$Z = \frac{x - \mu}{\sigma}$$

Question 4

A body temperature of 97.6°F is measured in a population with mean 98.0°F and standard deviation 0.7°F. What is the Z-score for this observation?

Accepted Answer

$$Z = \frac{97.6 - 98.0}{0.7} = -0.57$$

Question 5

Which of the following statements about boxplots is FALSE?

Accepted Answer

Boxplots use the minimum and maximum values to determine outliers.

Question 6

If a dataset is bell-shaped and symmetric, which rule can be used to estimate the percentage of data within one, two, and three standard deviations of the mean?

Accepted Answer

The Empirical Rule (68-95-99.7 Rule)

Question 7

Which of the following is NOT a criterion for determining the shape of a distribution?

Accepted Answer

Value of the IQR

Question 8

A histogram of the number of U.S. states visited by students is approximately symmetric. Which numerical summary is most appropriate for describing the center?

Accepted Answer

The mean

Question 9

Which of the following best describes the effect of outliers on the mean and median?

Accepted Answer

Outliers affect the mean more than the median

Question 10

Given a boxplot with an asterisk (*) beyond the whisker, what does this symbol represent?

Accepted Answer

An outlier

Question 11

If the mean is greater than the median in a dataset, what is the likely shape of the distribution?

Accepted Answer

Right-skewed

Question 12

Which of the following is true about Z-scores?

Accepted Answer

They have no units

Question 13

A dataset of body temperatures is approximately normal with mean $$98.0^\circF $$and standard deviation $$0.7^\circF. $$What percentage of observations are expected to fall between $$97.3^\circF $$and $$98.7^\circF$$?

Accepted Answer

68%

Question 14

Which of the following is a limitation of using the IQR as a summary statistic?

Accepted Answer

It may not be informative for bimodal or multimodal data

Question 15

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is used for categorical variables

Question 16

A student scores 1.5 standard deviations above the mean on a standardized test. What is their Z-score?

Accepted Answer

$$Z = 1.5$$

Question 17

Which of the following is a correct interpretation of a Z-score of -2?

Accepted Answer

The observation is 2 standard deviations below the mean

Question 18

Which of the following is a reason why the mean body temperature of humans has decreased over the past century, according to recent studies?

Accepted Answer

Changes in human physiology and improved health

Question 19

When comparing two groups using side-by-side boxplots, what can you learn that you cannot from a single boxplot?

Accepted Answer

Differences in center, spread, and outliers between groups

Boxplots, Outliers, Standardization, and the Normal Model: Study Notes for Statistics

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