Variance Sum Law I
Prerequisites
Variance
Learning Objectives
 Compute the variance of the sum of two uncorrelated variables
 Compute the variance of the difference between two uncorrelated
variables
As you will see in later sections, there are many
occasions on which it is important to know the variance of the
sum of two variables. Consider the following situation: (a) you
have two populations, (b) you sample one number from each population,
(c) you add the two numbers together. The question is, "What
is the variance of this sum."
It turns out that the variance of this sum can
be computed according to the following formula:
where the first term is the variance of the sum,
the second term is the variance of the males and the third term
is the variance of the females.
The formula for the variance of the difference between
the two variables (memory span in this example) is shown below.
Notice that expression for the difference is the same as the formula
for the sum.
More generally, the variance sum law can be written
as follows:
which is read "The variance of X plus or
minus Y is equal the variance of X plus the variance of Y.
The formulas for the sum and
difference of variables given above only apply when the variables
are independent.
The general form of the variance sum law is presented
in a section
in the chapter on correlation.
