Discrete Data — Definition, Formula & Examples
Discrete data is data you get by counting, so each value comes from a set of separate, specific possibilities, such as 0, 1, 2, or 3 pets. Values in between, like 2.4 pets, are not possible.
A quantitative variable is discrete if its set of possible values is finite or countably infinite, meaning the values can be listed as a first, second, third, and so on. Data recorded from a discrete variable are called discrete data. The opposite type is continuous data. A continuous variable can take any value in an interval of real numbers.
How It Works
To decide whether data are discrete, ask how the values were obtained. If you counted something (people, goals, cars, siblings), the data are discrete. If you measured something on a scale that can be divided as finely as you like (height, time, mass), the data are continuous. Classifying the data helps you pick a display. Discrete data fit naturally in a frequency table, dot plot, or bar graph, with one count for each possible value.
Worked Example
Problem: Ten students report how many siblings they have: 0, 1, 1, 2, 1, 3, 0, 2, 1, 4. Explain why these data are discrete, organize them in a frequency table, and find the mean number of siblings.
Step 1: Classify the data. Each value is a count of people, so only whole numbers are possible. You cannot have 1.5 siblings. The data are discrete.
Step 2: Count how often each possible value appears. The frequencies should add up to the 10 students.
Step 3: Find the total number of siblings. Multiply each value by its frequency and add the products.
Step 4: Divide the total by the number of students to get the mean.
Answer: The data are discrete because they are counts. The frequencies are 2, 4, 2, 1, 1 for 0 to 4 siblings, and the mean is 1.5 siblings. A mean of discrete data does not have to be one of the possible values.
Visualization
Why It Matters
Middle school statistics standards ask you to choose an appropriate display for a data set. That choice depends on whether the data are discrete or continuous. A bar graph or dot plot suits discrete data, and a histogram with grouped intervals suits continuous data. Later, in high school statistics and AP Statistics, the same split separates discrete probability distributions, such as the binomial distribution, from continuous ones like the normal distribution.
Common Mistakes
Mistake: Thinking that any data written as whole numbers must be discrete, for example calling heights rounded to the nearest centimeter discrete.
Correction: Rounding changes how a value is recorded, not what kind of variable it is. Height can take any value in a range, so it stays continuous even after rounding. Ask whether the quantity was counted or measured.
Mistake: Deciding that data are continuous just because they contain decimals, such as prices like $3.25.
Correction: Prices move in fixed steps of $0.01, so you can list every possible amount. That makes money amounts discrete. Look for separate, listable steps, not for the presence of a decimal point.