# Absolute frequency

Example of an absolute frequency distribution: Forecast of the age distribution for Germany in 2050

The term absolute frequency is synonymous with the colloquial term number. The absolute frequency is a measure of descriptive statistics and should be differentiated from the term relative frequency .

The absolute frequency is the result of a simple counting of objects or events (better elementary events ). It indicates how many elements with the same characteristic of interest were counted.

As a number , it can only be a natural number and cannot be negative. Because of its fixed zero point and fixed whole-number units, it is an absolute scale . This means that their zero point and the size of the units cannot be meaningfully changed. In contrast to the relative frequency, the values ​​of the absolute frequency are absolute, i.e. unchangeable. Their range of values ​​is from 0 to infinity.

In contrast, the absolute frequency is not suitable for comparing subsets of differently sized basic amounts. The level of the absolute frequency depends on the size of the basic set considered, which makes this comparison pointless. A standardized measure , the relative frequency, is therefore used for such a comparison .

## rule

If, when observing a random attempt or when checking a sample, the event occurs a total of times, then this quantity is called the absolute frequency of the event . The abbreviation for the relative frequency is . ${\ displaystyle n}$ ${\ displaystyle A}$${\ displaystyle H_ {n} (A)}$${\ displaystyle A}$${\ displaystyle h}$

## example

When considering symmetrical data, a previous classification is advisable . The absolute frequencies of the classes are then formed. In a survey 453 people are asked about their age. The count shows that 197 people fall into the class “from 20 years to under 30 years”. So the absolute frequency of this class is 197.

## Absolute frequency in medical statistics

The absolute frequency can be given instead of the probability in order to facilitate the understanding of risks and test results and is therefore used especially in statistics and probability calculations . The specification is made in " X of Y ", for example "8 of 1000". This information is a normalization of the natural frequency (for example "1 in 125").

Medical test results can be interpreted more easily by showing them in absolute frequencies. Bayes' theorem offers an alternative calculation .

An example ( without specifying probabilities)

• 10 out of 1000 symptom-free people have an illness (the so-called base proportion ). In 8 of the 10 people who have this disease, a special medical test is positive ( sensitivity = 810 = 80%), in 990 healthy people the test is positive in 99, i.e. only in 891 negative ( Specificity = 891990 = 90%). Question: How many of those examined with a positive result are actually sick?

A decision tree is helpful to visualize the problem.

A representation in the decision tree:

```                    1000
/      \
krank  /        \  gesund
/          \
10           990
/\            /\
/  \          /  \
− /    \ +    + /    \ −
/      \      /      \
2       8     99      891
```
• "+" ... positive test result
• "-" ... negative test result

Result : Of the 107 (= 8 + 99) people with a positive test result, only 8 people are actually sick, i.e. less than every 10th of the people examined. All of this without any other investigation.

Note: The results are obviously wrong for 101 people. 99 people are healthy but are considered sick in the test result (false positive) and 2 people are sick but are considered healthy in the test result (false negative).

This visualization of frequencies with a decision tree has the following advantages for understanding Bayes' theorem:

• Looking at sets and subsets (“8” of “10”) is often easier than calculating the probabilities in percent and the counter-probabilities.
• The translation into probabilities is omitted and the interpretation of the result is easier.
• Simplicity: there is no need to combine several rules, especially the difficult-to-understand inversion ( something should be said about from) in Bayes' theorem.${\ displaystyle P (A | B)}$${\ displaystyle P (B | A)}$
• Sequence argument. The hierarchical-sequential decisions are easy to represent.