Statistics

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# Relative Frequency

## 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, an NFL team has never played the Super Bowl in their home stadium. 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 NFL team plays the Super Bowl in their home stadium next year! But we also must remember that we calculated relative frequency to make this prediction, so it is not impossible that an NFL team plays the Super Bowl in their home stadium next year. 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.

### 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%.**