#statistics

Center describes a *typical value* of in a [[Data|data]] set.

# Types
## Mean
$$\huge mean = \frac{sum_{of values}}{number_{of values}}$$
Sample mean:
$$\LARGE \overline {X}=\frac{\sum X}{n}$$, where n is the [[Populations and samples|sample size]]. Sample mean depends on the sample

Population mean:
$$\LARGE \mu = \frac{\sum X}{N}$$, where N is the population size. Population mean is usually constant

The mean serves as the balance point for its frequency distribution, becuase the sum of all scores, expressed as positive and negative deviations from the mean, always equals zero:
![[Pasted image 20230827111401.png]]

## Median
The median is the middle value when the data is ordered in the ascending order:
- If the number of values is odd, the median is the middle value
- If the number of values is even, the median is the average of the two middle values

## Mode
The **mode** is the value that appears most often in a set of data values.

# Usage for different [[Data in statistics|data types]]
Quantitative data: mean, median, mode

Qualitative data: mode always appropriate, median sometimes appropriate (if the level of measurement is ordinal), do NOT use the mean with qualitative data:
![[Pasted image 20230827121840.png]]
![[Pasted image 20230827122040.png]]