#statistics 

**Normal curve** - a theoretical curve noted for its symmetrical bell-shaped form.

Most generalised [[Frequency distribution|distributions]] approximate the normal curve

## Properties
The value of the [[Measures of central tendency|mean, median, and mode]] is the same for the normal curve.
Since the normal curve is an idealised curve that is presumed to describe a [[Populations and samples|population]], then the symbols $\LARGE \mu$ and $\LARGE \sigma$ are used for the mean and [[Measures of central tendency|standard deviation]] respectively.

![[Pasted image 20230827185224.png]]
Obvious differences in appearance among normal curves are less important than they might seem, as because of their common mathematical origin, every normal curve can be interpreted in exactly the same way **once any distance from the mean is expressed in standard deviation units**.


## Use in approximating proportions
![[Pasted image 20230827184058.png]]
(shorter than exactly 66.0 inches)
![[Pasted image 20230827184115.png]]
(same, but more accurate)

## Standard normal curve and table
**Standard normal curve** - the tabled normal curve for [[Z scores]], with a mean of 0 and a standard deviation of 1 ^2a5640

If the original distribution approximates a normal curve, then the shift to z scores will always produce a new distribution that approximates the standard normal curve.
![[Pasted image 20230902183604.png]] ^577352

Essentially, the standard normal table consists of columns of z scores coordinated with columbs of proportions.
![[Pasted image 20230902183932.png]]
![[Pasted image 20230902184331.png]] ^72e350