AP - Statistics:: Exploring One-Variable Data

Statistics is best described as the study of:

- **A)** How to collect, organize, analyze, and draw conclusions from data, accounting for the natural variability present in real-world observations
- **B)** Only the calculation of averages
- **C)** Only probability theory, unrelated to real data
- **D)** A branch of algebra concerned solely with equations

A CATEGORICAL variable is one that:

- **A)** Takes numerical values that can be measured or counted (e.g., height, number of siblings)
- **B)** Places an individual into one of several groups or categories (e.g., eye color, political party)
- **C)** Can only take the values 0 or 1
- **D)** Is always ordered from smallest to largest

Which of the following is an example of a QUANTITATIVE variable?

- **A)** A student's favorite subject
- **B)** A student's eye color
- **C)** The number of hours a student studies per week
- **D)** A student's school (elementary, middle, high)

A quantitative variable is DISCRETE if:

- **A)** It is always categorical
- **B)** It only takes negative values
- **C)** It can only take a countable (often finite, or countably infinite) set of values, typically whole numbers, such as the number of pets owned
- **D)** It can take any value within an interval, such as height or weight

A RELATIVE FREQUENCY in a frequency table represents:

- **A)** The raw count of observations in a category
- **B)** The standard deviation of the data
- **C)** The proportion (or percentage) of the total observations that fall into a particular category, found by dividing that category's count by the total count
- **D)** The average of all the observations

A survey of 200 students found that 50 prefer online classes. What is the RELATIVE FREQUENCY of students preferring online classes?

- **A)** \(0.25\) (or 25%)
- **B)** \(50\)
- **C)** \(4\)
- **D)** \(0.50\)

In a two-way table, what is the difference between a MARGINAL relative frequency and a CONDITIONAL relative frequency?

- **A)** Marginal frequencies only apply to quantitative data
- **B)** They are always numerically identical
- **C)** A marginal relative frequency is based on the totals (row or column sums) relative to the grand total, while a conditional relative frequency is restricted to a single row or column (a subgroup), answering 'given this category, what proportion falls into that other category?'
- **D)** Conditional relative frequencies are always larger than marginal ones

In a two-way table, 80 out of 120 males prefer coffee over tea. What is the CONDITIONAL relative frequency of preferring coffee, GIVEN that the person is male?

- **A)** \(\dfrac{120}{80}\)
- **B)** \(80\)
- **C)** \(120\)
- **D)** \(\dfrac{80}{120} \approx 0.67\) (67%)