Table of Contents
Normal Distribution By James Grow
Distributions
Distributions
Distributions can be described by their median or half way point
Distributions can be described by their mean or balance point
The mean and the median or average need nor occur together
A normal distribution is symmetric with a center of symmetry
This center of symmetry will be a balance point
The median and the mean will be at the same point
Characterization is done by its mean and standard deviation
The mean or average can change
Without changing its shape
There is point where the tangent is infinity
This point marks a standard deviation
If s is increased broader, flatter curve will be produced
Take a normal distribution with a measuring stick s long
Area under this part of the curve, 1s long, is 68.3%
Area under curve 2s long is is 95.4
Area under curve with 3s is 99.7
Data for Distribution
Determine the sum of all observations
Divide by the number of observations
Determine the average or mean
Determine the variation from the average
Sum the square of these variations
Divide by the number of observations minus 1
To determine the Variance
Take the square root of the variance
To determine the Standard Deviation
Standard Deviation for a different set of observations
a 1.932 s Vs a 7.534 s
Normal Distribution
This is a Quincunx
A bearing can fall to the right
The second ball bearing can fall either way
Even to the left
Again to the left
This will produce a normal distribution
A large number of ball bearings will create a normal distribute
For a p=0.5 chance even a small number produce a normal distribution
The distribution will be askew if the odds are not 50/50
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Author: Compaq User
Email: Grow@adm.njit.edu
Home Page: http://www-ec.njit.edu/~grow/statisti.htm
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