<s>
In	O
mathematics	O
and	O
statistics	O
,	O
deviation	B-General_Concept
is	O
a	O
measure	O
of	O
difference	O
between	O
the	O
observed	O
value	O
of	O
a	O
variable	O
and	O
some	O
other	O
value	O
,	O
often	O
that	O
variable	O
's	O
mean	O
.	O
</s>
<s>
The	O
sign	O
of	O
the	O
deviation	B-General_Concept
reports	O
the	O
direction	O
of	O
that	O
difference	O
(	O
the	O
deviation	B-General_Concept
is	O
positive	O
when	O
the	O
observed	O
value	O
exceeds	O
the	O
reference	O
value	O
)	O
.	O
</s>
<s>
A	O
deviation	B-General_Concept
that	O
is	O
a	O
difference	O
between	O
an	O
observed	O
value	O
and	O
the	O
true	O
value	O
of	O
a	O
quantity	O
of	O
interest	O
(	O
where	O
true	O
value	O
denotes	O
the	O
Expected	O
Value	O
,	O
such	O
as	O
the	O
population	O
mean	O
)	O
is	O
an	O
error	O
.	O
</s>
<s>
A	O
deviation	B-General_Concept
that	O
is	O
the	O
difference	O
between	O
the	O
observed	O
value	O
and	O
an	O
estimate	O
of	O
the	O
true	O
value	O
(	O
e.g.	O
</s>
<s>
In	O
statistics	O
,	O
the	O
absolute	O
deviation	B-General_Concept
of	O
an	O
element	O
of	O
a	O
data	B-General_Concept
set	I-General_Concept
is	O
the	O
absolute	O
difference	O
between	O
that	O
element	O
and	O
a	O
given	O
point	O
.	O
</s>
<s>
Typically	O
the	O
deviation	B-General_Concept
is	O
reckoned	O
from	O
the	O
central	O
value	O
,	O
being	O
construed	O
as	O
some	O
type	O
of	O
average	O
,	O
most	O
often	O
the	O
median	O
or	O
sometimes	O
the	O
mean	O
of	O
the	O
data	B-General_Concept
set	I-General_Concept
:	O
</s>
<s>
Di	O
is	O
the	O
absolute	O
deviation	B-General_Concept
,	O
</s>
<s>
m(X )	O
is	O
the	O
chosen	O
measure	O
of	O
central	O
tendency	O
of	O
the	O
data	B-General_Concept
set	I-General_Concept
—	O
sometimes	O
the	O
mean	O
(	O
)	O
,	O
but	O
most	O
often	O
the	O
median	O
.	O
</s>
<s>
For	O
an	O
unbiased	O
estimator	O
,	O
the	O
average	O
of	O
the	O
signed	O
deviations	B-General_Concept
across	O
the	O
entire	O
set	O
of	O
all	O
observations	O
from	O
the	O
unobserved	O
population	O
parameter	O
value	O
averages	O
zero	O
over	O
an	O
arbitrarily	O
large	O
number	O
of	O
samples	O
.	O
</s>
<s>
However	O
,	O
by	O
construction	O
the	O
average	O
of	O
signed	O
deviations	B-General_Concept
of	O
values	O
from	O
the	O
sample	O
mean	O
value	O
is	O
always	O
zero	O
,	O
though	O
the	O
average	O
signed	O
deviation	B-General_Concept
from	O
another	O
measure	O
of	O
central	O
tendency	O
,	O
such	O
as	O
the	O
sample	O
median	O
,	O
need	O
not	O
be	O
zero	O
.	O
</s>
<s>
Statistics	O
of	O
the	O
distribution	O
of	O
deviations	B-General_Concept
are	O
used	O
as	O
measures	O
of	O
statistical	O
dispersion	O
.	O
</s>
<s>
Standard	B-General_Concept
deviation	I-General_Concept
is	O
the	O
frequently	O
used	O
measure	O
of	O
dispersion	O
:	O
it	O
uses	O
squared	B-General_Concept
deviations	I-General_Concept
,	O
and	O
has	O
desirable	O
properties	O
,	O
but	O
is	O
not	O
robust	O
.	O
</s>
<s>
Average	B-General_Concept
absolute	I-General_Concept
deviation	I-General_Concept
,	O
is	O
the	O
sum	O
of	O
absolute	O
values	O
of	O
the	O
deviations	B-General_Concept
divided	O
by	O
the	O
number	O
of	O
observations	O
.	O
</s>
<s>
Median	B-General_Concept
absolute	I-General_Concept
deviation	I-General_Concept
is	O
a	O
robust	O
statistic	O
,	O
which	O
uses	O
the	O
median	O
,	O
not	O
the	O
mean	O
,	O
of	O
absolute	O
deviations	B-General_Concept
.	O
</s>
<s>
Maximum	O
absolute	O
deviation	B-General_Concept
is	O
a	O
highly	O
non-robust	O
measure	O
,	O
which	O
uses	O
the	O
maximum	O
absolute	O
deviation	B-General_Concept
.	O
</s>
<s>
Deviations	B-General_Concept
have	O
units	O
of	O
the	O
measurement	O
scale	O
(	O
for	O
instance	O
,	O
meters	O
if	O
measuring	O
lengths	O
)	O
.	O
</s>
<s>
One	O
way	O
is	O
by	O
dividing	O
by	O
a	O
measure	O
of	O
scale	O
(	O
statistical	O
dispersion	O
)	O
,	O
most	O
often	O
either	O
the	O
population	B-General_Concept
standard	I-General_Concept
deviation	I-General_Concept
,	O
in	O
standardizing	O
,	O
or	O
the	O
sample	O
standard	B-General_Concept
deviation	I-General_Concept
,	O
in	O
studentizing	O
(	O
e.g.	O
,	O
Studentized	O
residual	O
)	O
.	O
</s>
<s>
One	O
can	O
scale	O
instead	O
by	O
location	O
,	O
not	O
dispersion	O
:	O
the	O
formula	O
for	O
a	O
percent	O
deviation	B-General_Concept
is	O
the	O
observed	O
value	O
minus	O
accepted	O
value	O
divided	O
by	O
the	O
accepted	O
value	O
multiplied	O
by	O
100%	O
.	O
</s>
