The varianceis the expected value of the squared deviations of each observation from the random variable's expected value. As an expected value, the variance uses the probability of each observation xito weight the associated squared deviation: [xi- E(X)]2. The formula for variance is:
ó2(X) = ó [xi- E(X)]2* P(xi)
The standard deviationis the positive square root of the variance. It may be represented by ó(X) or just ó.
Example:
Event
xi
P(xi)
xi* P(xi)
[xi- E(X)]2* P(xi)
Fall short of forecast
-.03
.20
-.0060
.000361
Meet forecast
.01
.45
.0045
.000003
Exceed forecast
.04
.35
.0140
.000265
 
 
E(X)
.0125
ó2(X) = .000629