## Relative Frequency Lesson

### What is Relative Frequency?

Relative frequency is how often something occurs. The general formula for relative frequency is given as:

**Relative frequency = event count/total count**

Since we divide how many times the event occurs by the total number of events that occurred, **the frequency of the event is relative to the total number of events**.

Using the relative frequency formula will always result in a decimal value ranging from 0 to 1. A relative frequency of 0 means the event never occurs. A relative frequency of 1 means the event occurs every time.

### Why use Relative Frequency?

Calculating relative frequency of an event can help us understand the event and predict the future. If we know that an event has happened 55% of the time in the past and we are calculating that from a sufficient data pool, we can predict that the event has roughly a 55% chance of happening in the future.

Often times we won't need to predict an exact percentage chance an event has of happening in the future and can instead make a general prediction. For example, as of May 2023, an NBA team has never come back from a 0-3 deficit in the playoffs to win the series. If we plug the data into our formula, we will get a relative frequency of 0.

Based on this frequency, we can definitely predict that it is *unlikely* an NBA team comes back from a 0-3 deficit in the playoffs to win a series! But we also must remember that we calculated relative frequency to make this prediction, so it is not impossible that an NBA team comes back from a 0-3 deficit in the playoffs to win a series sometime in the future. Relative frequency *is a calculation* of how likely something is to happen based on previous results. It is not a guarantee that something will or will not happen.

### How to Calculate Relative Frequency: Example Problem

A person opens their fridge door 17 times on a particular day. A bottle of ketchup falls out on 4 occasions. What is the relative frequency of the bottle of ketchup falling out when their fridge door is opened?

Solution:

- The total count is 17, and the event count is 4. Let's plug these values into the relative frequency general formula.
- Relative frequency = event count/total count
- Relative frequency = 4/17 = 0.2353
- Converting the relative frequency to a percentage:
- 100·0.2353 = 23.53%
**The relative frequency is 0.2353, or 23.53%.**