The Language of Variation: Variables Chapter Notes | AP Statistics - Grade 9 PDF Download

Types of Variables

• Categorical Variables: These represent qualities or attributes that can be grouped into categories, not numbers. Examples include car colors (e.g., red, blue, black), state names, or countries. Categorical data is often grouped for comparison.
• Quantitative Variables: These involve numerical measurements, such as the number of days, product prices, or ages. Quantitative data can be further divided into:
  • Discrete: Whole numbers, like the number of children in a family.
  • Continuous: Values within a range, like height, weight, or age, which can include decimals.

Quantitative data allows for calculations like averages, while categorical data is used for grouping and comparison.

Levels of Measurement

Variables are measured at different levels, which determine how they can be analyzed:

• Nominal: Categorical data with no inherent order, e.g., eye color or gender.
• Ordinal: Categorical data with a meaningful order but no consistent differences between ranks, e.g., customer satisfaction (low, medium, high).
• Interval: Quantitative data with equal intervals but no true zero, e.g., temperature in Celsius.
• Ratio: Quantitative data with equal intervals and a true zero, allowing ratios like "twice as much," e.g., weight or income.

Why Variability Matters

Categorical vs. Quantitative Variables: A Deeper Look

• Categorical Variables: Represent non-numerical categories, such as gender (male, female), race, or marital status (single, married). These cannot be ranked or quantified numerically.
• Quantitative Variables: Represent numerical values, either:
  • Continuous: Any value within a range, e.g., height (5.7 ft) or weight (150.2 lbs).
  • Discrete: Specific numerical values, e.g., number of siblings (1, 2, 3).

Identifying variable types is crucial because different statistical methods apply to each. For instance, chi-square tests analyze categorical data, while t-tests are used for continuous quantitative data (more on these in later units).

Examples of Categorical Variables

• Gender (male, female)
• Race (e.g., White, Black, Hispanic)
• Marital status (single, married, divorced)
• Employment status (employed, unemployed, self-employed)
• Education level (high school, bachelor’s degree, etc.)
• Political party (Republican, Democrat, Independent)
• Religion (Christian, Muslim, Hindu)
• Eye color (blue, brown, green)
• Hair color (blonde, brunette, red)
• Birthplace (United States, Canada, Mexico)

Examples of Quantitative Variables

• Age (e.g., 16, 34)
• Height (e.g., 5’2”, 180 cm)
• Weight
• Income
• Body mass index (BMI)
• Blood pressure
• Heart rate
• Hours of sleep
• Distance traveled
• Number of siblings

Example: Transportation Safety (1998 Data)

Key Terms Explained