Variables: Continuous and Discrete

A variable can be measured, but variables differ in how they vary. On this basis they fall into two types.

Continuous variable — can take any numerical value in a range: whole numbers ($1, 2, 3, \dots$), fractions ($\tfrac{1}{2}, \tfrac{2}{3}, \tfrac{3}{4}, \dots$) and even non-fractional values such as $\sqrt{2}=1.414$ or $\sqrt{3}=1.732$. As a child's height grows from 90 cm to 150 cm it passes through every value in between — 90.85 cm, 102.34 cm, 149.99 cm — so its values can be broken into infinitely fine gradations. Weight, time and distance are other continuous variables.

Discrete variable — can take only certain values, changing by finite "jumps" and skipping the values in between. The number of students in a class must be a whole number: it can be 25 or 26 but never 25.5, since half a student is meaningless. "Discrete" does not mean "never fractional", though — a variable taking values $\tfrac{1}{8}, \tfrac{1}{16}, \tfrac{1}{32}, \tfrac{1}{64}, \dots$ is still discrete, because it jumps from one listed fraction to the next and takes no value between two adjacent ones. …