In AP Statistics, a discrete variable is a quantitative variable that can take on a countable number of values (finite or countably infinite), like the number of text messages received daily, as opposed to a continuous variable, which can take infinitely many uncountable values.
A discrete variable is one of the two flavors of quantitative variables in AP Stats. Per the CED, it "can take on a countable number of values," and that number can be finite (like the number of siblings you have) or countably infinite (like the counting numbers 1, 2, 3, ...). The quick gut check is this: if you'd naturally figure out the value by counting, it's discrete. Number of cars in a parking lot, number of free throws made, number of texts received today. All counts, all discrete.
The contrast is a continuous variable, which can take infinitely many values that cannot be counted. No matter how close two values of a continuous variable are, there's always another possible value squeezed between them (between 5.2 seconds and 5.3 seconds sits 5.25, and between those sits 5.251, forever). With a discrete variable, there are gaps. Between 3 text messages and 4 text messages, there is nothing. You can't receive 3.5 texts.
Discrete variables live in Unit 1: Exploring One-Variable Data, specifically Topic 1.5 (Representing a Quantitative Variable with Graphs). Learning objective 1.5.A asks you to classify types of quantitative variables, which on the exam means looking at a described variable and labeling it discrete or continuous. That classification isn't busywork. It feeds directly into 1.5.B, representing quantitative data graphically, because the type of variable shapes which display makes sense. Discrete data with a small number of values often works beautifully in a dotplot, where identical values stack into neat columns, while continuous data usually gets binned into a histogram. The discrete/continuous distinction also comes back hard later in the course, since the entire structure of probability distributions in Unit 4 splits along this exact line.
Keep studying AP Statistics Unit 1
Continuous Variable (Unit 1)
This is the other half of the classification in LO 1.5.A, and the exam loves testing the pair together. Counts are discrete, measurements are continuous. Reaction time in milliseconds is continuous because between any two times there's always another possible time.
Histogram (Unit 1)
Histograms group values into intervals, which makes them the go-to display for continuous data or discrete data with lots of values. With a discrete variable, each bar can sit on a single value, but changing interval widths still changes the picture, so read the axis carefully.
Bar Graph (Unit 1)
A discrete variable's dotplot or histogram can look suspiciously like a bar graph, but bar graphs are for categorical data. The number of texts you got is a discrete quantitative variable; your phone's brand is categorical. The graph follows the variable type, not the other way around.
Discrete Random Variables (Unit 4)
The discrete/continuous split returns in Unit 4 with random variables. Probability distributions for discrete random variables (including the binomial and geometric) assign a probability to each countable value, so nailing the classification in Unit 1 pays off all course long.
This term shows up almost entirely as a classification task. A multiple-choice stem describes a variable in context, like "a researcher counts the number of text messages received daily," and asks what type of variable it is. The answer hinges on one move: ask whether the values are countable. Counts (texts, students, cars) are discrete; measurements (reaction time in milliseconds, height, temperature) are continuous. You'll also see the reverse, where a question lists four variables and asks which one is discrete or which one is continuous. No released FRQ asks you to define "discrete variable" outright, but FRQ Part A questions in Unit 1 expect you to choose and describe an appropriate graph for the data, and recognizing that a variable is discrete (and quantitative, not categorical) is step one of doing that correctly.
Both are quantitative, which is exactly why they get mixed up. A discrete variable takes a countable number of values with gaps between them (you can have 2 or 3 pets, never 2.7). A continuous variable can take infinitely many uncountable values, and between any two values there's always another one (reaction time, weight, distance). Shortcut: counted means discrete, measured means continuous. Watch out for the trap where a measurement gets recorded in whole numbers; age in years is typically treated as continuous because the underlying quantity is measured time, not a count.
A discrete variable is a quantitative variable that takes on a countable number of values, and that count can be finite or countably infinite.
If you find the value by counting (texts received, cars in a lot, students in a class), the variable is discrete; if you find it by measuring (time, weight, length), it's continuous.
The CED's test for continuous is that between any two values there's always another possible value; discrete variables have gaps where no values exist.
Discrete doesn't automatically mean whole numbers; the defining feature is countability, not integers.
Classifying a variable as discrete or continuous (LO 1.5.A) guides which graph fits it best (LO 1.5.B), with dotplots shining for discrete data with few values.
The discrete/continuous distinction returns in Unit 4, where discrete random variables get probability distributions that assign a probability to each individual value.
A discrete variable is a quantitative variable that can take on a countable number of values, like the number of text messages received daily or the number of students in a class. The number of possible values can be finite or countably infinite.
No. The defining feature is countability, not integers. Shoe sizes jump in half steps (8, 8.5, 9) and are still discrete because you can list every possible value. Most exam examples are counts, though, so whole numbers are the typical case.
A discrete variable takes a countable number of values with gaps between them, while a continuous variable takes infinitely many values that can't be counted, with another possible value between any two values. Number of texts is discrete; reaction time in milliseconds is continuous.
Discrete. You count text messages, and the possible values (0, 1, 2, 3, ...) are countable with nothing in between. This exact scenario is a classic AP Stats classification question.
No. A discrete variable is quantitative; its values are numbers you can do math with, like averaging the number of pets per household. A categorical variable sorts individuals into groups like eye color or phone brand, even if the categories are labeled with numbers (like jersey numbers).