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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?