<s>
The	O
five-number	B-Language
summary	I-Language
is	O
a	O
set	O
of	O
descriptive	B-General_Concept
statistics	I-General_Concept
that	O
provides	O
information	O
about	O
a	O
dataset	O
.	O
</s>
<s>
These	O
quartiles	O
are	O
used	O
to	O
calculate	O
the	O
interquartile	B-General_Concept
range	I-General_Concept
,	O
which	O
helps	O
to	O
describe	O
the	O
spread	O
of	O
the	O
data	O
,	O
and	O
determine	O
whether	O
or	O
not	O
any	O
data	O
points	O
are	O
outliers	O
.	O
</s>
<s>
In	O
order	O
for	O
these	O
statistics	O
to	O
exist	O
the	O
observations	O
must	O
be	O
from	O
a	O
univariate	B-General_Concept
variable	O
that	O
can	O
be	O
measured	O
on	O
an	O
ordinal	O
,	O
interval	O
or	O
ratio	O
scale	O
.	O
</s>
<s>
The	O
five-number	B-Language
summary	I-Language
provides	O
a	O
concise	O
summary	O
of	O
the	O
distribution	O
of	O
the	O
observations	O
.	O
</s>
<s>
The	O
five-number	B-Language
summary	I-Language
gives	O
information	O
about	O
the	O
location	O
(	O
from	O
the	O
median	O
)	O
,	O
spread	O
(	O
from	O
the	O
quartiles	O
)	O
and	O
range	B-General_Concept
(	O
from	O
the	O
sample	O
minimum	O
and	O
maximum	O
)	O
of	O
the	O
observations	O
.	O
</s>
<s>
Since	O
it	O
reports	O
order	B-General_Concept
statistics	I-General_Concept
(	O
rather	O
than	O
,	O
say	O
,	O
the	O
mean	O
)	O
the	O
five-number	B-Language
summary	I-Language
is	O
appropriate	O
for	O
ordinal	O
measurements	O
,	O
as	O
well	O
as	O
interval	O
and	O
ratio	O
measurements	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
quickly	O
compare	O
several	O
sets	O
of	O
observations	O
by	O
comparing	O
their	O
five-number	B-Language
summaries	I-Language
,	O
which	O
can	O
be	O
represented	O
graphically	O
using	O
a	O
boxplot	B-Application
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
points	O
themselves	O
,	O
many	O
L-estimators	O
can	O
be	O
computed	O
from	O
the	O
five-number	B-Language
summary	I-Language
,	O
including	O
interquartile	B-General_Concept
range	I-General_Concept
,	O
midhinge	B-General_Concept
,	O
range	B-General_Concept
,	O
mid-range	O
,	O
and	O
trimean	O
.	O
</s>
<s>
The	O
five-number	B-Language
summary	I-Language
is	O
sometimes	O
represented	O
as	O
in	O
the	O
following	O
table	O
:	O
</s>
<s>
This	O
example	O
calculates	O
the	O
five-number	B-Language
summary	I-Language
for	O
the	O
following	O
set	O
of	O
observations	O
:	O
0	O
,	O
0	O
,	O
1	O
,	O
2	O
,	O
63	O
,	O
61	O
,	O
27	O
,	O
13	O
.	O
</s>
<s>
So	O
the	O
five-number	B-Language
summary	I-Language
would	O
be	O
0	O
,	O
0.5	O
,	O
7.5	O
,	O
44	O
,	O
63	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
calculate	O
the	O
five-number	B-Language
summary	I-Language
in	O
the	O
R	B-Language
programming	I-Language
language	I-Language
using	O
the	O
fivenum	O
function	O
.	O
</s>
<s>
The	O
summary	O
function	O
,	O
when	O
applied	O
to	O
a	O
vector	O
,	O
displays	O
the	O
five-number	B-Language
summary	I-Language
together	O
with	O
the	O
mean	O
(	O
which	O
is	O
not	O
itself	O
a	O
part	O
of	O
the	O
five-number	B-Language
summary	I-Language
)	O
.	O
</s>
<s>
You	O
can	O
use	O
PROC	O
UNIVARIATE	B-General_Concept
in	O
SAS	B-Language
(	O
software	O
)	O
to	O
get	O
the	O
five	B-Language
number	I-Language
summary	I-Language
:	O
</s>
