_
174
_
,
THE BIOL£OGY OF FISHES
for exa'mple,the length of the caudal region, the motor part
of the sh.
-—In this way comparable numbers are obtained
Ÿ
Ï
for the measurable characters and theycan then be dealt _:'
with in,—the same way as the numerical characters.
,.
When the numbers have been obtained, they can be"
,
arranged in the following way. The
“
variants
”
are the
:
different observed
.
values of a character, e.g.
-
vertebræ ; the
“
frequencies
”
are the observed number of
:
individuals at each value.
As will be seen, the
î
_
group themselves about a central value, becoming fewer On ' '
‘
each side away from this value. The latter is called the
“
mode.”
The siniplest way of calculating the average *,
and higher moments is to take this mode as the central point
'
—
and, sum up
the total differences or
“
deviations
”
from it.
-
The
is then 0,“ and- the deviations from it are plus_0t Ï:;Î=_minüs according as the variants are above or below the mode.
We thus obtain the—following scheme. »
,
.
_
'
'
_
.
Sum of squares
."
Variants.
Frequencies.
’Deviations.
Jof_deviatîons.
*_
110
_
,
—..S
;
_
i
.
.
"25,
111
,
17
']— 68
272
112
.
89
,
=
"‘—3”
"
_
'
..801 «'
,
-
_,
1——_2'
,
:j—,*704,
—
1408
—
,
114
.
719
—
—
,
—I "
{.
.
‘7I,9
_
1_15
-*
«
oo
.
…
.—
.
-116
500
;
_
_
+î_ +soo *
500‘
;.
117
192
.
,
-
+2
,;
768_
_
,I-I8QJ
36
+3
"
9+iî08
324
=
119.
,.
.
4 »
.
.
,-:Î4Lë,iä
+16
,
64
"angthunfthdtn bytt1 numb
’
Ï Ï (2775)
:
wh1hmanthuhgf Hthfqunlby
.
>“
this
”thet{j»mode.: ThISgIVCSII473as :lthef
:
aver—age:ofçall=thefrequencres
:
_
,
.
represent the_.umber
;, .
,.
in açvery large conection
of 'Eels _f(Angüa vulgaris)
.
: ,}
tofb_e _mentiorîed’mthe ;
É
1 f
fbçènÿ'hÏàdè by Geerg Duncker ,
Ï Îg—1É
'
1
.:.
174
_
,
THE BIOL£OGY OF FISHES
for exa'mple,the length of the caudal region, the motor part
of the sh.
-—In this way comparable numbers are obtained
Ÿ
Ï
for the measurable characters and theycan then be dealt _:'
with in,—the same way as the numerical characters.
,.
When the numbers have been obtained, they can be"
,
arranged in the following way. The
“
variants
”
are the
:
different observed
.
values of a character, e.g.
-
vertebræ ; the
“
frequencies
”
are the observed number of
:
individuals at each value.
As will be seen, the
î
_
group themselves about a central value, becoming fewer On ' '
‘
each side away from this value. The latter is called the
“
mode.”
The siniplest way of calculating the average *,
and higher moments is to take this mode as the central point
'
—
and, sum up
the total differences or
“
deviations
”
from it.
-
The
is then 0,“ and- the deviations from it are plus_0t Ï:;Î=_minüs according as the variants are above or below the mode.
We thus obtain the—following scheme. »
,
.
_
'
'
_
.
Sum of squares
."
Variants.
Frequencies.
’Deviations.
Jof_deviatîons.
*_
110
_
,
—..S
;
_
i
.
.
"25,
111
,
17
']— 68
272
112
.
89
,
=
"‘—3”
"
_
'
..801 «'
,
-
_,
1——_2'
,
:j—,*704,
—
1408
—
,
114
.
719
—
—
,
—I "
{.
.
‘7I,9
_
1_15
-*
«
oo
.
…
.—
.
-116
500
;
_
_
+î_ +soo *
500‘
;.
117
192
.
,
-
+2
,;
768_
_
,I-I8QJ
36
+3
"
9+iî08
324
=
119.
,.
.
4 »
.
.
,-:Î4Lë,iä
+16
,
64
"angthunfthdtn bytt1 numb
’
Ï Ï (2775)
:
wh1hmanthuhgf Hthfqunlby
.
>“
this
”thet{j»mode.: ThISgIVCSII473as :lthef
:
aver—age:ofçall=thefrequencres
:
_
,
.
represent the_.umber
;, .
,.
in açvery large conection
of 'Eels _f(Angüa vulgaris)
.
: ,}
tofb_e _mentiorîed’mthe ;
É
1 f
fbçènÿ'hÏàdè by Geerg Duncker ,
Ï Îg—1É
'
1
.:.