A random variable is a variable whose possible values are outcomes of a random process.
There are two types of random variables:
- Discrete: Can take on only a countable number of distinct values like 0, 1, 2, 3, 50, 100, etc.
- Continuous: Can take on an infinite number of possible values like 0.03, 1.2374553, etc.
In this article we share 10 examples of random variables in different real-life situations.
Example 1: Number of Items Sold (Discrete)
One example of a discrete random variable is the number of items sold at a store on a certain day.
Using historical sales data, a store could create a probability distribution that shows how likely it is that they sell a certain number of items in a day.
For example:
| Number of Items | Probability |
|---|---|
| 0 | .004 |
| 1 | .023 |
| 2 | .065 |
| . . . | . . . |
The probability that they sell 0 items is .004, the probability that they sell 1 item is .023, etc.
Example 2: Number of Customers (Discrete)
Another example of a discrete random variable is the number of customers that enter a shop on a given day.
Using historical data, a shop could create a probability distribution that shows how likely it is that a certain number of customers enter the store.
For example:
| Number of Customers | Probability |
|---|---|
| 0 | .01 |
| 1 | .03 |
| 2 | .04 |
| . . . | . . . |
Example 3: Number of Defective Products (Discrete)
Another example of a discrete random variable is the number of defective products produced per batch by a certain manufacturing plant.
Using historical data on defective products, a plant could create a probability distribution that shows how likely it is that a certain number of products will be defective in a given batch.
For example:
| Number of Defective Products | Probability |
|---|---|
| 0 | .44 |
| 1 | .12 |
| 2 | .02 |
| . . . | . . . |
Example 4: Number of Traffic Accidents (Discrete)
Another example of a discrete random variable is the number of traffic accidents that occur in a specific city on a given day.
Using historical data, a police department could create a probability distribution that shows how likely it is that a certain number of accidents occur on a given day.
For example:
| Number of Traffic Accidents | Probability |
|---|---|
| 0 | .22 |
| 1 | .45 |
| 2 | .11 |
| . . . | . . . |
Example 5: Number of Home Runs (Discrete)
Another example of a discrete random variable is the number of home runs hit by a certain baseball team in a game.
Using historical data, sports analysts could create a probability distribution that shows how likely it is that the team hits a certain number of home runs in a given game.
For example:
| Number of Home Runs | Probability |
|---|---|
| 0 | .31 |
| 1 | .39 |
| 2 | .12 |
| . . . | . . . |
Example 6: Marathon Time (Continuous)
One example of a continuous random variable is the marathon time of a given runner.
This is an example of a continuous random variable because it can take on an infinite number of values.
For example, a runner might complete the marathon in 3 hours 20 minutes 12.0003433 seconds. Or they may complete the marathon in 4 hours 6 minutes 2.28889 seconds, etc.
In this scenario, we could use historical marathon times to create a probability distribution that tells us the probability that a given runner finishes between a certain time interval.
Example 7: Interest Rate (Continuous)
Another example of a continuous random variable is the interest rate of loans in a certain country.
This is a continuous random variable because it can take on an infinite number of values. For example, a loan could have an interest rate of 3.5%, 3.765555%, 4.00095%, etc.
In this scenario, we could use historical interest rates to create a probability distribution that tells us the probability that a loan will have an interest rate within a certain interval.
Example 8: Animal Weight (Continuous)
Another example of a continuous random variable is the weight of a certain animal like a dog.
This is a continuous random variable because it can take on an infinite number of values. For example, a dog might weigh 30.333 pounds, 50.340999 pounds, 60.5 pounds, etc.
In this case, we could collect data on the weight of dogs and create a probability distribution that tells us the probability that a randomly selected dog weighs between two different amounts.
Example 9: Plant Height (Continuous)
Another example of a continuous random variable is the height of a certain species of plant.
This is a continuous random variable because it can take on an infinite number of values. For example, a plant might have a height of 6.5555 inches, 8.95 inches, 12.32426 inches, etc.
In this case, we could collect data on the height of this species of plant and create a probability distribution that tells us the probability that a randomly selected plant has a height between two different values.
Example 10: Distance Traveled (Continuous)
Another example of a continuous random variable is the distance traveled by a certain wolf during migration season.
This is a continuous random variable because it can take on an infinite number of values. For example, a wolf may travel 40.335 miles, 80.5322 miles, 105.59 miles, etc.
In this scenario, we could collect data on the distance traveled by wolves and create a probability distribution that tells us the probability that a randomly selected wolf will travel within a certain distance interval.
Additional Resources
The following tutorials provide additional information about variables in statistics:
Introduction to Random Variables
What Are i.i.d. Random Variables?
What Are Levels of an Independent Variable?