#statistics 

A **frequency distribution** - a collection of [[Data|obsersvations]] produced by sorting observations into classes and showing their frequency (f) of occurrence in each class

Types:
- for ungrouped data - whenever observations are sorted into classes of *single values*
- for grouped data - whenever observations are sorted into classes of *multiple values*
- relative frequency distributions (see down)
- cumulative frequency distributions

## "Guidelines"
Essential:
- each observation should be included in one, and only one, class (130-139, 140-149, etc)
- list all classes, even those with zero frequences
- all classes should have equal intervals

optional:
- all classes should have both an upper boundary and a lower boundary
- select the class interval from convient numbers
- the lower boundary of each class interval should be a multiple of the class interval (130-139, class interval 10)
- aim for a total of approximately 10 classes

1C0☭ - essential
Domsub walks into a convenience store multiple times aiming in their heads - optional


## Class intervals
The **real limits** of class intervals are located at the midpoint of the gap between adjacent tabled boundaries (one-half of one unit of measurement below the lower tabled boundary and one-half of one unit of measurement above the upper tabled boundary)

e.g: the real limits for 140-149 are 139.5 and 149.5, the actual width of the class interval = 149.5-139.5 = 10

## Relative frequency distribution
**A frequency distribution showing the frequency of each class as a fraction of the total frequency for the entire distribution**
![[Pasted image 20230715223808.png]]

*They allow for a direct comparison of the shapes of different distribution without having to adjust for the different observation sizes*

## Cumulative frequency distribution
**Cumulative frequency distribution** - a frequency distribution showing the total number of observations in each class and all lower-ranked classes

Can be used effectively with sets of scores, such as test scores for intellectual or academic aptitude, when *relative standing* within the distribution assumes primary importance

![[Pasted image 20230722183751.png]]

#### Percentile ranks
**[[Percentile rank]] of an observation** - percentage of scores in the entire distribution with equal or smaller values than that score.

E.g. percentile rank of 80 - equal or lighters weights constitute 80 percent of the entire distribution

If we're dealing with grouped data, then we can assign percentile ranks to classes of observations instead of individual observations

## ![[Graphical representation of frequency distributions]]