Qualitative vs Quantitative Variables - Quick Reference

Qualitative vs Quantitative Variables

• Distinction:

  • Qualitative (categorical): describes categories or groups; non-numeric.

  • Quantitative (numerical): describes quantities; numeric values.

• Qualitative variables (examples):

  • Nationality

  • Level of education

  • Gender (observations: male or female) → categories

  • Data are non-numeric categories

• Quantitative variables (examples):

  • Number of children

  • Household income in the previous year

  • Daily intake of whole grains (grams per day)

  • Data are numeric values

Quantitative Variables: Discrete vs Continuous

• Quantitative Discrete Variable

  • Definition: a quantitative variable that has a finite number of possible values (countable)

  • Example: Number of students in each class

  • Key property: values are countable and separate

  • Note: often described as taking on distinct, separate values

• Quantitative Continuous Variable

  • Definition: a quantitative variable with an infinite number of possible values; can be measured to any desired precision

  • Example: Volume or mass (e.g., grams per day, volume of sound)

  • Key property: values fill an interval densely

• Quick classification rule

  • Discrete if values are countable (finite or countable many values)

  • Continuous if there are infinitely many possible values within a range (uncountable in practice)

Quick classification exercise (from study)

• Classify the following quantitative variables as discrete or continuous:

  • a. Number of children → discrete

  • b. Household income in the previous year → continuous

  • c. Daily intake of whole grains (grams per day) → continuous

Data and observations

• The list of observations a variable assumes is called data

• Example: Gender is a qualitative variable; observations are categories:

  • \{\text{male}, \text{female}}\

  • Data can be non-numeric (qualitative) or numeric (quantitative)