USEFUL NOTATIONS
Sample mean of size
n
.
Those notations are going to be used in EXAM 1 and they are going to be used in subsequent
material covered in this course. This is a standard notation used in STA2023 and it is printed
on the last page on the cover of your course books among other formulas.
If we consider sample of size
n
the elements of our sample usually have notation
X
1
,X
2
,...,X
n
.
For example if we have a sample that consists of four elements
p
3
,
4
,
1
,
0
q
then
X
1
3
,X
2
4
,X
3
1
and
X
4
0
.
Sample mean is just an average. The notation usually used is
¯
X
. So
¯
X
X
1
X
2
¤ ¤ ¤
X
n
n
Here three dots
...
mean that that we did not write numbers in between but that all
X
i
are
in numerator. That is we have the sum of
n
numbers in the numerator. For our example the
average (sample mean) is
¯
X
3
4
1
0
4
2
.
For big sample sizes
n
this notation is inconvenient and long. Therefore all books are using
short notation using
Σ
(Capital sigma letter from Greek alphabet) that stands for the sum.
It is just a short notation. So we have
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 Summer '08
 TA
 Statistics, 1J, 1 °

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