<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
(	O
univariate	O
)	O
is	O
a	O
measure	O
of	O
statistical	O
dispersion	O
equal	O
to	O
the	O
average	O
absolute	O
difference	O
of	O
two	O
independent	O
values	O
drawn	O
from	O
a	O
probability	O
distribution	O
.	O
</s>
<s>
A	O
related	O
statistic	O
is	O
the	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
,	O
which	O
is	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
divided	O
by	O
the	O
arithmetic	O
mean	O
,	O
and	O
equal	O
to	O
twice	O
the	O
Gini	O
coefficient	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
also	O
known	O
as	O
the	O
absolute	B-General_Concept
mean	I-General_Concept
difference	I-General_Concept
(	O
not	O
to	O
be	O
confused	O
with	O
the	O
absolute	O
value	O
of	O
the	O
mean	O
signed	O
difference	O
)	O
and	O
the	O
Gini	B-General_Concept
mean	I-General_Concept
difference	I-General_Concept
(	O
GMD	O
)	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
sometimes	O
denoted	O
by	O
Δ	O
or	O
as	O
MD	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
defined	O
as	O
the	O
"	O
average	O
"	O
or	O
"	O
mean	O
"	O
,	O
formally	O
the	O
expected	O
value	O
,	O
of	O
the	O
absolute	O
difference	O
of	O
two	O
random	O
variables	O
X	O
and	O
Y	O
independently	O
and	O
identically	O
distributed	O
with	O
the	O
same	O
(	O
unknown	O
)	O
distribution	O
henceforth	O
called	O
Q	O
.	O
</s>
<s>
For	O
a	O
random	O
sample	O
of	O
size	O
n	O
of	O
a	O
population	O
distributed	O
uniformly	O
according	O
to	O
Q	O
,	O
by	O
the	O
law	O
of	O
total	O
expectation	O
the	O
(	O
empirical	O
)	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
of	O
the	O
sequence	O
of	O
sample	O
values	O
yi	O
,	O
i	O
=	O
1	O
to	O
n	O
can	O
be	O
calculated	O
as	O
the	O
arithmetic	O
mean	O
of	O
the	O
absolute	O
value	O
of	O
all	O
possible	O
differences	O
:	O
</s>
<s>
The	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
quantifies	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
in	O
comparison	O
to	O
the	O
size	O
of	O
the	O
mean	O
and	O
is	O
a	O
dimensionless	O
quantity	O
.	O
</s>
<s>
The	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
equal	O
to	O
twice	O
the	O
Gini	O
coefficient	O
which	O
is	O
defined	O
in	O
terms	O
of	O
the	O
Lorenz	O
curve	O
.	O
</s>
<s>
This	O
relationship	O
gives	O
complementary	O
perspectives	O
to	O
both	O
the	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
and	O
the	O
Gini	O
coefficient	O
,	O
including	O
alternative	O
ways	O
of	O
calculating	O
their	O
values	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
invariant	O
to	O
translations	O
and	O
negation	O
,	O
and	O
varies	O
proportionally	O
to	O
positive	O
scaling	O
.	O
</s>
<s>
The	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
invariant	O
to	O
positive	O
scaling	O
,	O
commutes	O
with	O
negation	O
,	O
and	O
varies	O
under	O
translation	O
in	O
proportion	O
to	O
the	O
ratio	O
of	O
the	O
original	O
and	O
translated	O
arithmetic	O
means	O
.	O
</s>
<s>
If	O
a	O
random	O
variable	O
has	O
a	O
positive	O
mean	O
,	O
then	O
its	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
will	O
always	O
be	O
greater	O
than	O
or	O
equal	O
to	O
zero	O
.	O
</s>
<s>
If	O
,	O
additionally	O
,	O
the	O
random	O
variable	O
can	O
only	O
take	O
on	O
values	O
that	O
are	O
greater	O
than	O
or	O
equal	O
to	O
zero	O
,	O
then	O
its	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
will	O
be	O
less	O
than	O
2	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
twice	O
the	O
L-scale	O
(	O
the	O
second	O
L-moment	O
)	O
,	O
while	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
the	O
square	O
root	O
of	O
the	O
variance	O
about	O
the	O
mean	O
(	O
the	O
second	O
conventional	O
central	O
moment	O
)	O
.	O
</s>
<s>
The	O
differences	O
between	O
L-moments	O
and	O
conventional	O
moments	O
are	O
first	O
seen	O
in	O
comparing	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
and	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
(	O
the	O
first	O
L-moment	O
and	O
first	O
conventional	O
moment	O
are	O
both	O
the	O
mean	O
)	O
.	O
</s>
<s>
Both	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
and	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
measure	O
dispersion	O
—	O
how	O
spread	O
out	O
are	O
the	O
values	O
of	O
a	O
population	O
or	O
the	O
probabilities	O
of	O
a	O
distribution	O
.	O
</s>
<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
is	O
not	O
defined	O
in	O
terms	O
of	O
a	O
specific	O
measure	O
of	O
central	O
tendency	O
,	O
whereas	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
defined	O
in	O
terms	O
of	O
the	O
deviation	O
from	O
the	O
arithmetic	O
mean	O
.	O
</s>
<s>
Because	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
squares	O
its	O
differences	O
,	O
it	O
tends	O
to	O
give	O
more	O
weight	O
to	O
larger	O
differences	O
and	O
less	O
weight	O
to	O
smaller	O
differences	O
compared	O
to	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
.	O
</s>
<s>
When	O
the	O
arithmetic	O
mean	O
is	O
finite	O
,	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
will	O
also	O
be	O
finite	O
,	O
even	O
when	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
infinite	O
.	O
</s>
<s>
The	O
recently	O
introduced	O
distance	O
standard	B-General_Concept
deviation	I-General_Concept
plays	O
similar	O
role	O
to	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
but	O
the	O
distance	O
standard	B-General_Concept
deviation	I-General_Concept
works	O
with	O
centered	O
distances	O
.	O
</s>
<s>
+	O
Examples	O
of	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
and	O
relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
Distribution	O
Parameters	O
Mean	O
Standard	B-General_Concept
deviation	I-General_Concept
Mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
Relative	O
mean	B-General_Concept
absolute	I-General_Concept
difference	I-General_Concept
Continuous	O
uniform	O
Normal	O
;	O
undefined	O
Exponential	O
Pareto	O
;	O
Gamma	O
;	O
†	O
†	O
Gamma	O
;	O
Gamma	O
;	O
Gamma	O
;	O
Gamma	O
;	O
Bernoulli	O
Student	O
's	O
t	O
,	O
2	O
d.f.	O
</s>
