<s>
In	O
statistics	O
,	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
(	O
MAE	O
)	O
is	O
a	O
measure	O
of	O
errors	O
between	O
paired	O
observations	O
expressing	O
the	O
same	O
phenomenon	O
.	O
</s>
<s>
MAE	O
is	O
calculated	O
as	O
the	O
sum	B-General_Concept
of	I-General_Concept
absolute	I-General_Concept
errors	I-General_Concept
divided	O
by	O
the	O
sample	O
size	O
:	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
uses	O
the	O
same	O
scale	O
as	O
the	O
data	O
being	O
measured	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
is	O
a	O
common	O
measure	O
of	O
forecast	O
error	O
in	O
time	O
series	O
analysis	O
,	O
sometimes	O
used	O
in	O
confusion	O
with	O
the	O
more	O
standard	O
definition	O
of	O
mean	B-General_Concept
absolute	I-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
is	O
one	O
of	O
a	O
number	O
of	O
ways	O
of	O
comparing	O
forecasts	O
with	O
their	O
eventual	O
outcomes	O
.	O
</s>
<s>
Well-established	O
alternatives	O
are	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
scaled	I-General_Concept
error	I-General_Concept
(	O
MASE	O
)	O
and	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
.	O
</s>
<s>
Where	O
a	O
prediction	O
model	O
is	O
to	O
be	O
fitted	O
using	O
a	O
selected	O
performance	O
measure	O
,	O
in	O
the	O
sense	O
that	O
the	O
least	B-Algorithm
squares	I-Algorithm
approach	O
is	O
related	O
to	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
,	O
the	O
equivalent	O
for	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
is	O
least	B-General_Concept
absolute	I-General_Concept
deviations	I-General_Concept
.	O
</s>
<s>
MAE	O
is	O
not	O
identical	O
to	O
root-mean	B-General_Concept
square	I-General_Concept
error	I-General_Concept
(	O
RMSE	B-General_Concept
)	O
,	O
although	O
some	O
researchers	O
report	O
and	O
interpret	O
it	O
that	O
way	O
.	O
</s>
<s>
MAE	O
is	O
conceptually	O
simpler	O
and	O
also	O
easier	O
to	O
interpret	O
than	O
RMSE	B-General_Concept
:	O
it	O
is	O
simply	O
the	O
average	O
absolute	O
vertical	O
or	O
horizontal	O
distance	O
between	O
each	O
point	O
in	O
a	O
scatter	O
plot	O
and	O
the	O
Y	O
=	O
X	O
line	O
.	O
</s>
<s>
This	O
is	O
in	O
contrast	O
to	O
RMSE	B-General_Concept
which	O
involves	O
squaring	O
the	O
differences	O
,	O
so	O
that	O
a	O
few	O
large	O
differences	O
will	O
increase	O
the	O
RMSE	B-General_Concept
to	O
a	O
greater	O
degree	O
than	O
the	O
MAE	O
.	O
</s>
<s>
Provided	O
that	O
the	O
probability	O
distribution	O
of	O
X	O
is	O
such	O
that	O
the	O
above	O
expectation	O
exists	O
,	O
then	O
m	O
is	O
a	O
median	O
of	O
X	O
if	O
and	O
only	O
if	O
m	O
is	O
a	O
minimizer	O
of	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
with	O
respect	O
to	O
X	O
.	O
</s>
<s>
This	O
optimization-based	O
definition	O
of	O
the	O
median	O
is	O
useful	O
in	O
statistical	O
data-analysis	O
,	O
for	O
example	O
,	O
in	O
k-medians	B-Algorithm
clustering	I-Algorithm
.	O
</s>
