<s>
In	O
statistics	O
,	O
a	O
sampling	B-General_Concept
distribution	I-General_Concept
or	O
finite-sample	O
distribution	O
is	O
the	O
probability	O
distribution	O
of	O
a	O
given	O
random-sample-based	O
statistic	O
.	O
</s>
<s>
If	O
an	O
arbitrarily	O
large	O
number	O
of	O
samples	O
,	O
each	O
involving	O
multiple	O
observations	O
(	O
data	O
points	O
)	O
,	O
were	O
separately	O
used	O
in	O
order	O
to	O
compute	O
one	O
value	O
of	O
a	O
statistic	O
(	O
such	O
as	O
,	O
for	O
example	O
,	O
the	O
sample	O
mean	O
or	O
sample	O
variance	O
)	O
for	O
each	O
sample	O
,	O
then	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
is	O
the	O
probability	O
distribution	O
of	O
the	O
values	O
that	O
the	O
statistic	O
takes	O
on	O
.	O
</s>
<s>
In	O
many	O
contexts	O
,	O
only	O
one	O
sample	O
is	O
observed	O
,	O
but	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
can	O
be	O
found	O
theoretically	O
.	O
</s>
<s>
Sampling	B-General_Concept
distributions	I-General_Concept
are	O
important	O
in	O
statistics	O
because	O
they	O
provide	O
a	O
major	O
simplification	O
en	O
route	O
to	O
statistical	O
inference	O
.	O
</s>
<s>
The	O
sampling	B-General_Concept
distribution	I-General_Concept
of	O
a	O
statistic	O
is	O
the	O
distribution	O
of	O
that	O
statistic	O
,	O
considered	O
as	O
a	O
random	O
variable	O
,	O
when	O
derived	O
from	O
a	O
random	O
sample	O
of	O
size	O
.	O
</s>
<s>
The	O
sampling	B-General_Concept
distribution	I-General_Concept
depends	O
on	O
the	O
underlying	O
distribution	O
of	O
the	O
population	O
,	O
the	O
statistic	O
being	O
considered	O
,	O
the	O
sampling	O
procedure	O
employed	O
,	O
and	O
the	O
sample	O
size	O
used	O
.	O
</s>
<s>
There	O
is	O
often	O
considerable	O
interest	O
in	O
whether	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
can	O
be	O
approximated	O
by	O
an	O
asymptotic	O
distribution	O
,	O
which	O
corresponds	O
to	O
the	O
limiting	O
case	O
either	O
as	O
the	O
number	O
of	O
random	O
samples	O
of	O
finite	O
size	O
,	O
taken	O
from	O
an	O
infinite	O
population	O
and	O
used	O
to	O
produce	O
the	O
distribution	O
,	O
tends	O
to	O
infinity	O
,	O
or	O
when	O
just	O
one	O
equally-infinite-size	O
"	O
sample	O
"	O
is	O
taken	O
of	O
that	O
same	O
population	O
.	O
</s>
<s>
The	O
distribution	O
of	O
these	O
means	O
,	O
or	O
averages	O
,	O
is	O
called	O
the	O
"	O
sampling	B-General_Concept
distribution	I-General_Concept
of	O
the	O
sample	O
mean	O
"	O
.	O
</s>
<s>
This	O
distribution	O
is	O
normal	O
(	O
n	O
is	O
the	O
sample	O
size	O
)	O
since	O
the	O
underlying	O
population	O
is	O
normal	O
,	O
although	O
sampling	B-General_Concept
distributions	I-General_Concept
may	O
also	O
often	O
be	O
close	O
to	O
normal	O
even	O
when	O
the	O
population	O
distribution	O
is	O
not	O
(	O
see	O
central	O
limit	O
theorem	O
)	O
.	O
</s>
<s>
When	O
calculated	O
from	O
the	O
same	O
population	O
,	O
it	O
has	O
a	O
different	O
sampling	B-General_Concept
distribution	I-General_Concept
to	O
that	O
of	O
the	O
mean	O
and	O
is	O
generally	O
not	O
normal	O
(	O
but	O
it	O
may	O
be	O
close	O
for	O
large	O
sample	O
sizes	O
)	O
.	O
</s>
<s>
In	O
such	O
cases	O
the	O
sampling	B-General_Concept
distributions	I-General_Concept
may	O
be	O
approximated	O
through	O
Monte-Carlo	B-Algorithm
simulations	I-Algorithm
,	O
bootstrap	B-Application
methods	I-Application
,	O
or	O
asymptotic	O
distribution	O
theory	O
.	O
</s>
<s>
standard	B-General_Concept
error	I-General_Concept
of	O
that	O
quantity	O
.	O
</s>
<s>
For	O
the	O
case	O
where	O
the	O
statistic	O
is	O
the	O
sample	O
mean	O
,	O
and	O
samples	O
are	O
uncorrelated	O
,	O
the	O
standard	B-General_Concept
error	I-General_Concept
is	O
:	O
</s>
<s>
where	O
is	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
population	O
distribution	O
of	O
that	O
quantity	O
and	O
is	O
the	O
sample	O
size	O
(	O
number	O
of	O
items	O
in	O
the	O
sample	O
)	O
.	O
</s>
<s>
For	O
the	O
case	O
where	O
the	O
statistic	O
is	O
the	O
sample	O
total	O
,	O
and	O
samples	O
are	O
uncorrelated	O
,	O
the	O
standard	B-General_Concept
error	I-General_Concept
is	O
:	O
</s>
<s>
where	O
,	O
again	O
,	O
is	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
population	O
distribution	O
of	O
that	O
quantity	O
and	O
is	O
the	O
sample	O
size	O
(	O
number	O
of	O
items	O
in	O
the	O
sample	O
)	O
.	O
</s>
<s>
Population	O
Statistic	O
Sampling	B-General_Concept
distribution	I-General_Concept
Normal	O
:	O
Sample	O
mean	O
from	O
samples	O
of	O
size	O
n	O
.	O
</s>
<s>
If	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
not	O
known	O
,	O
one	O
can	O
consider	O
,	O
which	O
follows	O
the	O
Student	O
's	O
t-distribution	O
with	O
degrees	O
of	O
freedom	O
.	O
</s>
