You will learn in this guide how to find frequency, what is meant by absolute and relative frequency and how to calculate them.

It is important, including for *calculating probability*, that you know how to find frequency and the difference between the **absolute** and the **relative frequency**. You will use these two terms very often when describing *probability* *theory** *experiments, but also when dealing with *percentages*.

Tip: We’ll look at absolute and relative frequencies in a moment. You do not need a lot of previous knowledge. However, it helps if you already know what a chance experiment is, and the basic difference between absolute frequency and relative frequency.

To better understand the **difference between absolute and relative frequency** , we will explain this using a simple example: Imagine you have two different sized candy bags in front of you. Both bags contain yellow, green and red candies. You especially like the green candies and you want to know how many green candies are in the big and small bags. To find out, you can simply count the green candies.

#### Absolute frequency

You find there are nine green candies in the large candy bag and only six in the small bag.

You have just determined the absolute frequency of green candies in two bags of different sizes. So the absolute frequency simply indicates the number of green candies. You can get the absolute frequency by simply counting it – you don’t have to calculate. In most cases, the absolute frequency is given in whole numbers (also called absolute numbers).

**The absolute frequency describes the number of elements or objects with a certain characteristic. It is determined by counting and is usually given as a whole number.**

#### Relative frequency

The difference between the relative and the absolute frequency is already in the name: *relative* means something like ” *proportionate”* or *“dependent on certain conditions”. *But to what quantity can we put the frequency in relation?

Let’s look again at our example with the green candies. We have already noticed that there are fewer candies in the small bag. Since we examined two different sized candy bags, it is of course also important for us to know how many green candies there are in relation to the contents of the whole bag. To find out, we first need to find the total number of candies in the two bags.

We now know the number of green candies (absolute frequency) and the total number of candies per bag. Now we can easily calculate the relative frequency of the green candies:

large bag: 9/36= 0,25 =ˆ 25 %

small bag: 6/12= 0,5 =ˆ 50 %

The relative frequency puts the absolute number of an event in relation to the whole. It is given in percent and therefore has a value between 0 and 1 in decimal notation.

The relative frequency is therefore nothing else than what you may already know under the term of the *relative proportion*. If we look again at our results, we can see that the absolute frequency of the green candies in the large bag is higher, but the relative frequency there is lower. So now we understand how to find frequency, it is clear that it is more worthwhile to buy many small bags than a few large ones.

## How to find frequency: ex**planation of absolute frequency**

Let’s start with the absolute frequency. The definition:

**The absolute frequency H _{n} (x) of an event x means how often x occurs within a sample of size n.**

**Example 1: Absolute frequency**

We take a normal 6-sided cube dice. We roll it a few times and keep a tally of how often which number comes up. The tally sheet then looks like this.

How high is the absolute frequency of the numbers? We count the number of lines for the dice results 1 to 6. The absolute frequency simply indicates how often which number was thrown:

- The absolute frequency of the number 1 is 5.
- The absolute frequency of the number 2 is 4.
- The absolute frequency of the number 3 is 5.
- The absolute frequency of the number 4 is 8.
- The absolute frequency of the number 5 is 3.
- The absolute frequency of the number 6 is 5.

The “formula” that is often sought here does not exist in this sense. The expression H _{n} (x) is to be understood as follows: We add up the number of throws: 5 + 4 + 5 + 8 + 3 + 5 = 30. So we have n = 30. This is our lower case n according to H. The result of the dice comes in brackets, i.e. 1 to 6. And after the equals (=) how often a dice result has been cast.

- H
_{30}(1) = 5 - H
_{30}(2) = 4 - H
_{30}(3) = 5 - H
_{30}(4) = 8 - H
_{30}(5) = 3 - H
_{30}(6) = 5

## How to find **relative frequency**

The absolute frequency just showed how often something happened. In the example above, the number 4 was rolled a total of 8 times. But is that a lot or a little now? To be able to assess this, there is also the relative frequency. This indicates the proportion of the whole. When rolling the number 4 from the example, this would be 8 throws out of 30 throws as a relative frequency.

But let’s first look at a definition of relative frequency:

**The relative frequency h _{n} (x) is obtained by dividing the absolute frequency H _{n} (x) by the number of attempts n.**

Relative frequency formula :

**Example 2: Relative frequency**

We take the dice attempt from above again and calculate the relative frequency for the numbers 1 to 6. First we need to know how often in total the dice were thrown. We add all the lines together. This is a total of 30. The number is 30, in short n = 30. We already know the absolute frequencies, because we have already given them above (are the blue numbers in the picture).

We divide the absolute frequency by the number — here 30 — and get the relative frequency.

Relative frequencies of the dice attempt :

There is also a little check to test if you have the correct answers. If you add up the relative frequencies, the total is 1. Alternatively, you can also specify the relative frequencies in percent. To do this, simply multiply the values by 100. For example 0.1667 would become 16.67%.

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