Probability and Statistics > Descriptive Statistics> > What is a Discrete Variable?

## What is a Discrete Variable?

A **variable** is a quantity that has changing values. A **discrete variable** is a variable that can only take on a **certain number of values**. In other words, they don’t have an infinite number of values. If you can count a set of items, then it’s a discrete variable. The opposite of a discrete variable is a continuous variable. Continuous variables can take on an infinite number of possibilities.

### What is a Discrete Variable? Examples

Some examples of discrete variables:

**Number of quarters in a purse, jar, or bank.**Discrete because there can only be a certain number of coins (1,2,3,4,5…). Coins don’t come in amounts of 2.3 coins or 10 1/2 coins, so it isn’t possible for there to be an infinite number of possibilities. In addition, a purse or even a bank is restricted by size so there can only be so many coins.**The number of cars in a parking lot.**A parking lot can only hold a certain number of cars.**Points on a 10-point rating scale.**If you’re graded on a 10-point scale, the only possible values are 1,2,3,4,5,6,7,8,9, and 10.**Ages on birthday cards.**Birthday cards only come in years…they don’t come in fractions. So there are a finite amount of possibilities (presumably, about one hundred).

### What is a Discrete Variable? Discrete random variables

Discrete *random* variables are variables that are a result of a random event. For example, the roll of a die. Discrete random variables are represented by the letter X and have a probability distribution P(X). If you flipped a coin two times and counted the number of tails, that’s a discrete random variable. It’s represented by the letter X. X in this case can only take on one of three possible variables: 0, 1 or 2 [tails].

**Next:**

Discrete vs continuous variables.

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