Types of Data

Pre-Algebra · Axiom Academy

Every variable splits down two yes/no questions into categorical, discrete, or continuous — learn to route any data to its branch. 1. The First Fork: Categorical vs Numerical Collect any variable and ask one question: can you do meaningful arithmetic with its values? Numerical data are quantities you can add, compare, and average. Categorical data are labels that name a group — you can count how many fall in each label, but adding or averaging the labels themselves is meaningless. Numerical: the average is a real number Categorical: "average color" has no meaning 2. The Second Fork: Discrete vs Continuous Once data is numerical, ask the second question: do you count it or measure it? Discrete data comes from counting — it lands on separated values with gaps between them (you can have 3 siblings or 4, never 3.5). Continuous data comes from measuring — it can take any value in a range, as precise as your tool allows. Whole-number tallies: siblings, students in a class, goals scored, a dice roll. Values sit on isolated pegs. Height, weight, time, distance, temperature. Zoom in and there's always a value between any two. Is there a smallest step between possible values? Gaps discrete. No gaps continuous. "Shoe size 9" counts off a list (discrete); "foot length 26.4 cm" is measured (continuous). "Number of children: 0, 1, 2, 3…" snaps to whole pegs — discrete . "A child's height: 1.05 m, 1.052 m, 1.0521 m…" never has to stop — continuous . Same people, two different kinds of data.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.