Variance of a discrete random variable Var(X)
variance is a measure of the spread(dispersion) of a set of data points around their mean value.
Mathematically, the variance is the expectation( mean) of the averageof the squared deviations from the mean.
xr is any value of the random variable x
μ is the mean value of x
n is the number of values of x
Σ means the sum of all values in the brackets
Variance and Expected Values
Variance can also be written in terms of the expectation operator E( ) :
This can be expanded and consolidated to another form:
substituting for E[X] from μ = E[X]
So the mean μ , the variance Var(X) and the standard deviation σ (sigma) are all related to one another.
Var(X) = σ2
Variance and linearity
In a similar way to the Expectation Operator for E[aX + b] , the Variance Operator Var( ) behaves in a similar, though not identical, fashion.
E[aX + b] = aE(X) + b
however, Var(aX + b) = a2 Var(X)
This can be derived from first principles.
using (from above)
and replacing X with aX+b,
since, Var(X) = E[X2] - E[X]2
then, Var(aX + b) = a2 Var(X)
|stand. deviation 1|
|stand. deviation 2|
|stand. deviation 3|
|goodness of fit|
|distrib. sample mean|
|mean,median comprd 1|
|mean,median comprd 2|
|type I & II errors|
|Edxl S1 Statistics spec.|
|Edxl S1 Statistics ans.|
|Edxl S2 Statistics spec.|
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|Edxl S3 Statistics spec.|
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