# Standard Deviation & Mean

## Mean, Standard Deviation, and Variability

Mean = Decribe the avarage.

Standard Deviation (S or SD) = Decribes the variablity

Variability = The amount by which participants vary or differ from each other.

## Example:

Group A: 0,5,10,15,20,25,30 (M=15.00, SD=10.00

Group B: 14,14,14,15,16,16,16 (M=15.00, SD=0.93)

Group C: 15,15,15,15,15,15,15 (M=15.00, SD=0.00)

* As you can see groups are the same on avarage, but differ in terms of variability.

* As a rule the smaller the variability the smaller the deviation is.

## Standard Deviation/Normal Curve

• The standard deviation has a special rlationship to the normal curve.
• If a distribution is normal, 68% of the participants in the distribution lie within one standard deviation unit of the mean plus or minus.

## Remember This:

• When a researcher is calculating the standard deviation, he or she is actually calulating the number of points that one must go out from the mean to capture 68%.
• 68% does not apply if the distribution is not normal.