Standard Deviation
Standard Deviation:
is a measure of the amount of dispersion in a set of values
measures the distance of values from the mean of the set of values
is the square root of its variance
is often represented by the lower case greek symbol for sigma
is approximated by the 68-95-99.7 Rule
Normal Distribution Example
The graph below illustrates Standard Deviation applied to a Normal Distribution:
68-95-99.7 Rule
The 68-95.99.7 Rule (aka: 68-95-100 Rule) is a shorthand for the percentage of values that lie within Standard Deviation bands around the Mean in a Normal Distribution.
1 band: approximately 68%
2 bands: approximately 95%
3 bands: approximately 99.7% or rounded to 100%
Standard Score (Z-score)
The Standard Score (aka: z-score) is the number of standard deviations by which the value of a measured data point is above or below the mean value, for example:
3 sigma = 3.0 standard score
2 sigma = 2.0 standard score
1 sigma = 1.0 standard score
0 sigma = 0 standard score
-1 sigma = -1.0 standard score
-2 sigma = -2.0 standard score
-3 sigma = -3.0 standard score
Mean and Variance
Mean and Variance values change the shape of the probability distribution: