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Quiz: Introduction to Statistics

Test your understanding of foundational statistics concepts with these review questions.

1. What is the primary purpose of statistics?

  1. To create complex mathematical formulas
  2. To collect, organize, analyze, and interpret data to make decisions
  3. To prove that one group is better than another
  4. To memorize numerical facts about populations
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The correct answer is B. Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions or predictions. It helps us draw reasonable conclusions from information we can gather, even when we cannot know everything about a situation with complete certainty.

Concept Tested: Statistics

2. A researcher wants to know the average height of all high school students in Texas. She measures the heights of 500 randomly selected students. What are the population and sample in this study?

  1. Population: the 500 students; Sample: all Texas high school students
  2. Population: all Texas high school students; Sample: the 500 students measured
  3. Population: all students in the United States; Sample: the 500 students measured
  4. Population: the 500 students; Sample: only the tall students
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The correct answer is B. The population is the entire group you want to study or make conclusions about (all Texas high school students). The sample is the subset you actually collect data from (the 500 students measured). We use the sample to make inferences about the population.

Concept Tested: Population and Sample

3. Which of the following is an example of a categorical variable?

  1. Height in inches
  2. Number of siblings
  3. Blood type
  4. Temperature in degrees Fahrenheit
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The correct answer is C. Blood type (A, B, AB, O) is a categorical variable because its values are category names or labels, not numbers with mathematical meaning. Height and temperature are quantitative (continuous), while number of siblings is quantitative (discrete).

Concept Tested: Categorical Variable

4. A student's phone number is 555-867-5309. What type of variable is phone number?

  1. Quantitative discrete
  2. Quantitative continuous
  3. Categorical
  4. Both quantitative and categorical
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The correct answer is C. Even though phone numbers consist of digits, they are categorical variables because the numbers serve as labels, not quantities with mathematical meaning. You would not average phone numbers or say one phone number is "greater than" another in any meaningful way.

Concept Tested: Categorical Variable vs. Quantitative Variable

5. Which of the following is a discrete quantitative variable?

  1. The time it takes to run a mile
  2. A person's weight
  3. The number of text messages sent today
  4. The temperature outside
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The correct answer is C. The number of text messages is discrete because it can only take specific, separated values (0, 1, 2, 3...) and represents a count. Time, weight, and temperature are continuous because they can take any value within a range and arise from measurements.

Concept Tested: Discrete Variable

6. The average test score for ALL students at a university is 78.5. This value is called a:

  1. Statistic
  2. Parameter
  3. Sample
  4. Variable
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The correct answer is B. A parameter is a number that describes something about the population. Since this average describes ALL students at the university (the entire population of interest), it is a parameter. A statistic would describe only a sample of students.

Concept Tested: Parameter

7. A researcher calculates the average income of 200 randomly selected adults. This calculated average is a:

  1. Population
  2. Parameter
  3. Sample
  4. Statistic
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The correct answer is D. A statistic is a number that describes something about a sample. Since the average was calculated from 200 selected adults (a sample), not from all adults in the population, it is a statistic. Statistics are used to estimate unknown population parameters.

Concept Tested: Statistic

8. In a study examining whether exercise affects blood pressure, which variable would be the explanatory variable?

  1. Blood pressure
  2. Exercise amount
  3. Age of participants
  4. Heart rate
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The correct answer is B. The explanatory variable (also called the independent variable) is the variable we think might explain or influence changes in another variable. Exercise amount is what we think might affect blood pressure (the response variable). The explanatory variable is the potential cause.

Concept Tested: Explanatory Variable

9. Each row in a dataset containing information about students (name, age, GPA, and major) represents:

  1. A variable
  2. An observation
  3. A parameter
  4. A statistic
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The correct answer is B. An observation (also called a case or record) contains the values of all variables for one individual. Each row in a dataset represents one observation, such as all the information collected about one particular student. The columns represent variables.

Concept Tested: Observation

10. What does a distribution describe?

  1. The total number of observations in a dataset
  2. The difference between a parameter and a statistic
  3. The pattern of values a variable takes and how often each value occurs
  4. The relationship between explanatory and response variables
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The correct answer is C. A distribution describes the pattern of values that a variable takes on, including what values are possible and how often each value occurs. It tells us about the center, spread, and shape of the data, answering questions like "What's typical?" and "How spread out are the values?"

Concept Tested: Distribution