Question 1

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

Accepted Answer

A parameter describes a characteristic of a population, while a statistic describes a characteristic of a sample.

Question 2

A researcher records the number of siblings each student in a class has. What type of variable is this, and is it discrete or continuous?

Accepted Answer

Quantitative, discrete

Question 3

Which of the following graphs would be most appropriate to display the distribution of a single categorical variable?

Accepted Answer

Bar chart

Question 4

Given the following data set: $$\{2, 4, 4, 6, 8, 10, 12\}$$, what is the median?

Accepted Answer

$$6$$

Question 5

A distribution is left-skewed. Which of the following is most likely true about the relationship between the mean and the median?

Accepted Answer

The mean is less than the median.

Question 6

A company wants to compare the variability in quarterly returns between two mutual funds. Which measure should they use to compare the spread of the data, and why?

Accepted Answer

Standard deviation, because it measures the average distance from the mean.

Question 7

Suppose the heights (in cm) of a group of adults are normally distributed with a mean of $$170$$ and a standard deviation of $$10. $$What is the $$z-$$score for a person who is $$185 cm $$tall?

Accepted Answer

$$z = 1.5$$

Question 8

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the sample size increases, the sample mean approaches the population mean.

Question 9

A quality control manager randomly selects $$50$$ bottles of soda from a production line of $$10,000$$ bottles. The average fill volume of these $$50$$ bottles is a:

Accepted Answer

Statistic

Question 10

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are independent, what is the probability that both $$A$$ and $$B$$ occur?

Accepted Answer

$$0.15$$

Question 11

A pie chart is best used for which type of data?

Accepted Answer

Categorical

Question 12

Given the following five-number summary for a data set: $$\{10, 20, 30, 40, 100\}$$, which measure of center is most resistant to the outlier?

Accepted Answer

Median

Question 13

A student scores $$2$$ standard deviations above the mean on a standardized test. What percentage of students scored lower than this student, assuming a normal distribution?

Accepted Answer

About $$97.5\%$$

Question 14

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to extreme values.

Question 15

A contingency table is used to:

Accepted Answer

Display the relationship between two categorical variables.

Question 16

A boxplot is especially useful for:

Accepted Answer

Displaying the five-number summary and identifying outliers.

Question 17

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

Accepted Answer

Mean = Median = Mode

Question 18

A researcher wants to know if there is an association between gender (male/female) and preference for a new product (like/dislike). Which statistical tool should be used?

Accepted Answer

Contingency table

Question 19

Suppose you flip a fair coin three times. What is the probability of getting exactly two heads?

Accepted Answer

$$0.375$$

Question 20

Which of the following best describes an event that is considered 'unusual' in statistics?

Accepted Answer

An event with a probability less than $$0.05$$

Foundations of Descriptive Statistics and Probability: Study Guide

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