Averaging and Probability Distributions
Example data set:
x
i
__
6
3
4
6
6
3
7
8
6_
49
average = x
–
=
∑
x
i
n
=
49
9
= 5.44
Using a weighted average: weight each result by the number of
occurrences, n
i
.
n
6
x
6
↓↓
average = x
–
=
∑
n
i
x
i
∑
n
i
=
2(3)+1(4)+0(5)+4(6)+1(7)+1(8)
2+1+0+4+1+1
=
49
9
with the sum over all possible values of x.
Using a probability distribution P(x
i
):
Weight each result by the probability of its occurrence.
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 Weighted mean, pi xi, example data

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