INSTRUCTIONS 
FOR LENGTH-WEIGHT 
PROGRAMS for
IBM 1620 in FORTRAN-FORMAT 
(FORTRAN I)
Wayne E. Swingle
Zoology-Entomology 
Department Series
Fisheries No. 1
AGRICULTURAL EXPERIMENT 
STATION
AUBURN UNIVERSITY
or, September 1964
E. V. Smith, Directc
Auburn, Alabama
r
Instructions for Length-Weight Programs
for
IBM 1620
in
Fortran/Format (Fortran I)
by
Wayne E. Swingle*
INTRODUCTION
The need for tables and equations expressing the relationship between length
and weight of a species of fish arises frequently in fisheries work. At certain
times, it is impractical to take measurements of both length and weight since the
apparatus used for weighing is not accurate enough to weigh the smaller specimens.
Also, errors in recording or weighing under field conditions occasionally make
it necessary to substitute estimated 
weights for field data. In such cases,
tables expressing the average weight for a given length are invaluable.
Equations relating length and weight are useful for comparing populations,
for examining growth differences of fish subjected 
to different treatment effects,
for calculating condition factors, and for determining Von Bertalanffy growth
equations in terms of weight.
The author, through this set of computer programs, has attempted to remove
some of the tedious labor associated with the tabulation of length-weight relation-
ships. He has attempted to make this set of programs as versatile as possible.
Because the present trend is toward reporting length-weight relationships in
inches and pounds, the programs are designed to convert other units of measure
to inches and pounds. However, the programs will ccmpute equations and empirical
From a thesis submitted as partial requirement for M. S. degree in Fisheries
Management.
relations in terms of other units provided the specifications 
given in the
subsequent sections are followed.
Program I computes two length-weight equations, Program II tabulates 
empir-
ical relationships including average weight, maximum weight, minimum 
weight
and the condition index. Program III transforms data cards in units 
other than
inches and pounds to data in inches and pounds. Detailed descriptions 
of the
programs are given in the sections that follow.
DESCRIPTIONS OF PROGRAMS
Program I
Title: Length-Weight Relationships of Fishes I, IBM 1620, Fortran/Format
This program computes the standard length-weight equations and also a third
degree polynomial equation by least-squares procedures as outlined by Hader and
Grandage (1958). Input may include measurement data of individual 
specimens or
of many specimens combined in class intervals for which the average is computed
and considered as one observation. The output consists of: a) estimates of the
parameters of the three equations,
log (W) * log (a) + b log 
(L) (1)
W = aLb (2)
W = b
I 
+ b
2
L + b
3
L
2 
+ b4L
3  
(3)
b) for equation (1), the standard error, correlation coefficient, means, intercept,
sums of squares of the observations and deviations, and the numbers of fish and
observations (one observation may include many fish where class intervals are used);
c) for equation (3), the X'X matrix of the normal equations, the forward abbre-
viated Doolittle solution of this matrix, and the inverse of the X'X matrix; 
d)
estimated weights by 1-inch intervals using equations (2) and (3).
The program utilizes 1600 storage positions. Data cards are processed 
at the
rate of 37 per minute with calculations and punch out requiring an additional 
3
minutes. Estimates of the parameters are accurate to at least four significant
figures.
Options: Measurement data may be in inches-pounds, inches-ounces, inches-
grams, millimeters-pounds and millimeters-grams; output is in inches-pounds, or
output may be in same units as measurement data. Computation of the third degree
polynomial is under control of a header card and may be omitted. Data of mixed
systems of measurement may be entered and a single equation 
with output in inches-
pounds is computed.
Restrictions: Input and output are on cards with one data card required for
each observation. Input is limited to length measurements up to 5 digits (or 4
digits and a decimal), weight measurements up to 10 digits, and 8 digits are
available for number of fish per class interval (where class intervals are used
the weight must be the total weight of all fish in that interval). Estimated
weights from the fitted equations are limited to 99 length-integer intervals
(for inches, weights may be obtained for fish 1 to 99 inches by one-inch intervals).
Source Proaram
1 SUMX2=0O
SUMY2-O
SUMVYO
SUMXUO
SUMXY=O
TOTN=O
SFNO=0O
SWYaO
SWX-O
SWX2=O
SWX3=O
SWX4=0O
SWX5O
SWX6=0
SWXY=0
SWX2Y=0
SWX3Y=0
200 READ5,MSETLSETJSET
5 FORMAT(I2.3X.lllXI11)
2 READ 99,SIZEFNOTOTWTPBNOKI
99 FORMAT(F5.2,F8.0'F10.5,F4.0,44XI1)
IF(SIZE-8888. )
2
0.20l
4
20 IF(KI-1)21,21,200
21 IF(TOTWT)2392*23
23 IF(SIZE)25,2,25
25 IF(FNOt22,2.22
22 AVGWT=TOTWT/FNO
TF(LSET-1) 10591O59100
100 TF(LSET-3)1O691O7*1O1
101 IFCLSET-5)10891099105
105 WY=AVGWT
WX=S IZE
GO TO 6
106 WY=AVGWT/453*59
WX=SIZE/25*4
GO TO 6
107 WY=AVGWT
WX=SIZE/2594
GO TO 6
108 WY=AVGWT/453.59
WX=SIZE
GO TO 6
109 WY=AVGWT/1690
WX=S IZE
GO TO 6
6 Y=LOG(WY)*.43429448
X=LOG(WX )** 43429448
SUMX2=SUMX 2+X*X
SUMX=SUMX+X
SUMY2zSUMY 2+Y*Y
SUMY=SUMY+Y
SUMXY=SUMXY +X*Y
TOTN=TOTN+1.o
SFNO=SFNO+FNO
Swx =Swx+wx
swy =swy+wy
SWX2=SWX 2+WX*WX
SWX 3=SWX 3+WX*WX*WX
SWX4= SWX4+WX*WX*WX*WX
SWX 5=SWX 5+WX*WX*WX*WX*WX
SWX6=SWX 6+WX*WX*WX *WX*WX*WX
SwxY=Swxv+wx*wY
SWX2Y=SWX2Y+WX*WX*WY
SWX3Y=SWX3Y+WX*WX*WX*Wy
GO TO 2
14 CTX=SUMX**2/TOTN
CTY=SUMY**2 /TOTN
CTXY= (SUMX*SUMY) / TOTN
SSX2=SUMX2-CTX
SSY2=SUMY2-CTY
SSXY=SIJMXY-CTXY
86 FORMAT( 3HSY,9E12*6,4HSY2,9E12e6)
PUNCH 879~SD
87 FORMAT(3HSD=9E12o6)
PUNCH 139R9AVGXtAVGY
13 FORMAT( 1OHCORR COEF=,F10.6,5HAVGX=,F12.8,5HAVGY,9F12.8).
PUNCH4
PUNCH 96,SFNOpPBNO,5SSX2ioSSY2
96 FORMAT( 5HSFNO=,F1O.O,5HPBNO,9F6.O,5HSSX2=,F12.6,5HSSY2,tF12.6).
PUNCH4
PUNCH979T N *SSXY
97 FORMAT( 5HTOTN=,F8.O ,5HSSXY=,F12.6)
PUNCH4
PUNCH88,B9A 9ALOG
88 FORMAT( 2HB=,F1O.5,2HA=,F12.8,5HALOG=,F12.5)
PUNCH4
PUNCH 449S
44 FORMAT(1OHSTD ERROR=9F12*8)
PUNCH4
PUNCH34*SWX ,SWXZSWX3,SWX4
PUNCH4
34 FORMAT( 5HSUMXnE12.6,6HSUMX2,9E12.6w6HSUMX3=,E2696HSUMX4x9E12.6)
35 FORMAT(6HSUMX5,9E12.6,6HSUMX6= 9E12.695HSUMY,9E12.6)
PUNCH359SWX59SWX69,SWY
PUNCH4
PUNCH36 ,SWXY ,SWX2Y ,SWX3Y
PUNCH4
36 FORMAT (6HSUMXYtE12.6 7HSUMX2YtE12.6 7HSUMX3Ya 
'E12.6)
IF(JSET-1 )37,37,38
38,81=0
B2=0
B3=0
B4=0
GO TO 76
37 A11=TOTN
A12=SWX
A13=SWX2
A14=SWX3
GI1=SWY
81 1uTOTN/TOTN
812 =SWX/TOTN
81 3SWX2/TOTN
B 14=SWX3/TOTN
G 12=SWY/TOTN
A22=SWX2-A12*B12
A23=SWX3-A12*813
A24=SWX4-Al12*B14
G21=SWXY-A12*G12
B22 J wA22/' 1A22 '
844=A44/A44
G 42=G4l /A44
PUNCH39
-6-
39 FORMAT(26HDOOLITTLE FORWARD SOLUTION)-
PUNCH4OA11 .A129A139A14,G11
40 FORMAT(5E12.6)
PUNCH4OB11 9B129B139Bl49G1.2
PUNCH41,A22 .A239A249G21
41 FORMAT(12X,4E12*6)
PUNCH41 ,822 ,B239B24 ,G22
PUNCH42 9A3 3 *A34 9G3.1
42 FORMAT(24X93E12*6)
PUNCH42 983 3 9B34 9G3 2
PUNCH43 .A44 vG41
43 FORMAT(36X92E12*6)
PUNCH439B44 9G42
B4=G42
B 3G32-B4*B34
B2=G22-B3*B23-B4*B24
Bl1G12-B2*B12-B3*B13-B4*Bl4
PUNCH4
PUNCK789B1 ,B29B39B4
78 FORMAT( 3H81,tE12.6,3HB2=,E12.6,3HB3=,E12.6,3HB4=,E12.6)
PUNCH4
C44=1 O/A44
C 34=-B34*C44
C24=-B23*C34-B24*C44
C 14=--B12*C24-B13*C34-mB14*C44
C331.O0/A33-B34*C34
C23w-'B23*C33-wB24*C34
C 13c.-B12*C2 3-B13*C33-B14*C34
C221 O/A22-B23*C23-B24*C24
C 12=-B12*C2 2-B13*C23-B14*C24
C 11=1.0/Al1-B2*C12-B13*C13-B14*Cl4
PUNCH45
45 FORMAT(23HDOOLITTLE BACK SOLUTION)
PUNCH46*C1 C129C13,C14
46 FORMAT (4E12 96)
PUNCH479C22 9C239C24
47 FORMAT(12X93E12*6)
PUNCH48YC33 9C34
48 FORMAT(24X92E12*6)
PWNCH49, C44
49'FORMAT(36X,E12*6)
76 PUNCH77
77 FORMAT(14X,6HLENGTH,4X,3HWT1,6X,3HWT2)
K=MSET
PUNCH4
PUNCH4
GO TO 1
END
-7-
Card Format
1) A Header Card precedes the deck of data 
cards and sets control parameters in
the program.
a. Columns 1 and 2 (Format 12) instructs 
the program to substitute integer
values of length into fitted equations,
W = aLb 
(2)
W = b
I 
+ b
2
L + b3L
2 
+ bLL
3  
(3)
with L = ]. to m (where m is the value typed into columns 1 and 2), and
to print out these values and the values 
of weight for each equation.
Examples: Column 1 2
Example: 0 9 - substitutes length integers from
1 to 9 into equations
Example: 9 9 - substitutes length integers from
1 to 99 into equations
b. Columns 3, h, and 5 are left blank.
c. Column 6 (Format Ii) instructs the program 
to change units to inches and
pounds before computation of equations (2) and 
(3) and their statistical
parameters.
Number
placed in Transformation
Column
6 Input data-----------------Output
1 or blank Output in same units as 
input
(use for data in inches-pounds)
2 millimeters-grams to 
inches-pounds
3 millimeters-pounds to inches-pounds
h inches-grams to 
inches-pounds
5 inches-ounces to inches-pounds
d. Column 7 is left blank
e. Column 8 instructs the program to include or delete computation of
equation (3) and print out of parameters and abbreviated Doolittle
solution of equation (3).
Examples: 1. When left blank computations of equation (3)
are included in output.
2. A numeral 2 in column 8 deletes above computation from
output.
2) A Subheader Card instructs the program that the next card will be a header
card or other than a data card. This card is used only where two or more
systems of measurements are used to compute a single equation. All columns
are blank on this card except a 2 must be typed in column 72.
3) Data Cards - Format (F5.2, F8.0, F10.5, Fh.O)
a. Columns 1 through 5, Format (F5.2) contain values of length. The values
may be in any units with or without decimal fractions. A decimal must
be typed in or else it is assumed to lie between columns 3 and h. (For
inch-group where the inch-integer is the midpoint, it is suggested that
the decimal be typed in column 5, which allows using the same data cards
for Program II - This also applies to length measures in centimeter-
integers)
Examples: Columns 1 2 3 h 5
Intended Number Number interpreted as:
5 5 . 5.ooooooo
5 5 So. oooooo
5 Data card rejected
S S . o 0 0 S.0oooooo
0.0 0 . 0 Data card rejected
-9-
b. Columns 6 through 13, Format 
(F8.0), contain the number of fish per
length-group. If there is only 
one fish for each length-group, 
1.0 must
be typed in these columns. 
Data cards with blanks or 
zeros are rejected.
Example: Columns 6 7 8 9 10 11 12 13
Intended 
Number interpreted
number 
as
2 
2 20.000000
2 
2 2.0000000
2h45 2 4 5 .
245.00000
2 
2 . 2.0000000
2h45 2 4 5 
2450oooo0.0
c. Columns 14 through 23, Format 
(F10.5) contain the total weight of 
all
fish in columns 6 through 13. Any 
unit of weight may be used. Unless 
a
decimal is typed in, it is assumed to lie between 
columns 18 and 19.
Data cards expressing trace by zero are rejected,
d. Columns 24 through 27, Format (F4.0) 
contain a problem number (an identi-
fication number for the researcher) limited 
to 3 digits and a decimal -
THIS NEED NOT BE TYPED ON DATA CARDS IF IT IS TYPED ON TRAILER CARD.
e. The remaining columns do not enter 
the computation; hence any coding
system or additional data may be entered 
in these spaces. However, it
is suggested that any identification numbers be placed 
in columns 73
through 80.
4) Additional Notes: (1) This program 
deletes cards with zeros or blanks 
for
values of length or weight or the number 
of fish from the computations;
therefore, blank cards of a different 
color may be used to separate data
cards into groups. (2) It is suggested 
that decimals be typed in for all
values. (3) To use program III that 
transforms units in millimeters-
grams, millimeters-pounds, inches-grams, 
inches-ounces, and inches-pounds
-..0 -
into inch-groups and pounds, columns 1, 6, 14, 28, and 31 must be blank
on the data cards.
5) A trailer card instructs the computer that a problem is over and clears the
memory for the next problem:
a) dolumns 1 through 5 must have 9999. typed in.
b) Columns 6 through 23 are blank.
c) Columns 24 through 27 must have the problem number typed in and limited
to 4 digits or 3 digits and decimal.
Loading Sequence When data for one problem are all in the same units, the sequence
of cards through the IBM 1620 is as follows:
( A. Object program deck
( B. Header card for problem 1
1. ( C. Data Deck for problem 1
( D. Trailer card for problem 1
( E. Header card for problem 2
2. ( F. Data Deck for problem 2
( G. Trailer card for problem 2
( H. Header card for problem 3
3. ( I. Data Deck for problem 3
( J. Trailer card for problem 3
n. (ZZZC. Header card for problem n
(ZZZD. Data Deck for problem n
(ZZZE. Trailer card for problem n
When data for a problem are of mixed units, the sequence of cards through the
the IBM 1620 is as follows:
( A. Object program deck
( B. Header card for problem 1 (a 2 in column 6)
( C. Data Deck for problem 1 (Units in mm-gm)
1. ( D. Subheader card for problem 1
( E. Header card for problem 1 (a 3 in column 6)
( F. Data Deck for problem 1 (units in mm-lbs)
( G. Trailer card for problem 1
-11-
( H. Header card for problem 2 (column 6 blank)
( I. Data Deck for problem (units in inches-lbs)
2. ( J. Subheader card for problem 2
( K. Header card for problem 2 (a 5 in column 6)
( L. Data Deck for problem 2 (units 
in inches-ounces)
( M. Trailer card for problem 2
n. ZZZC. Header card for problem n
ZZZD. Data Deck for problem n
ZZZE. Trailer card for problem n
The above sequence is merely an example; any combination of different units
may be used in a single problem as long as the data deck for each group of units
is preceeded by the correct header card as specified under card format for program
I, lc. and by a subheader card.
Output
The following table is the answer sheet obtained by processing the answer
cards through an IBM accounting machine. The symbol or symbols to the left of
an equals sign are as the computer prints out. To the right of the equals sign,
the author has chosen to place the appropriate statistical symbol or else an
explanation. Numerical answers would normally appear to the right of the equals
sign and would be of two forms, a number consisting of an integer and decimal
fraction or else as exponential numbers of the form .324505E+0h, .324505E-00,
and .324505F-02, which would be interpreted as follows: 3245.05, .324505, and
0.00324505, respectively. The first eight lines of output are derived from the
logarithmic forms of length and weight, whereas the next 16 lines of output are
derived from the length and weight not transformed to logarithms. A capital E
is used to represent the symbol sigma.
1) Printed Output
Line
1. SX =EX SX2 = EX
2  
SXY = EXY
2. SY = EY SY2 = EY
2
-12 -
SD 
= Ed 
2
CORR COEF =r AVGX =x AVGY= y
SFO Tta N.Fish;PBNO = problem no .;SSX2 = Ex
2  
SSY2 = Ey
2
tOTN = number of' observations (n);SSXY= Exy
7.* B=b;A =a;ALOG =log
10 
a
8. STD ERROR = Sy.x
9. SU1Y( 
EX SUNX2= 
EX
2
10. SUNX'5;=EX
5 
SUMX6 nEX
6
11. SUNXY = EXY SUN2Y n EX
2
Y
DOOLITTL~E FOWJARD SOLUTION
12. A
00  
A
0 1  
A
0 2  
A
0 3  
A
13. B 
00  
B 
01  
B
02  
B 
03  
E
ih. A 
11
A
12
A 
13
A
SUNX3 = EX
3
SUNMY = EY
S UMX 3Y =EX 
3
Y
surxh = EXh
L
0
y
BOY
41Y
B B
11 12
A
22
B
22
B
13
A
23
B
23
A
3 3
B
33
B
ly
A
2Y
B1 =b, B2=b
2  
B3 =b 
3  
B4L=bh4
DOOLITTLE BACK SOLUTION
CO 00 col 
C0
2  
Co0
3
C
11  
C
1 2  
C
13
C C
22 23
C
33
LENGTH WTl WT2 Where WT1 = weight calculated by equation (2) and
WT2 = weight calculated by equation (3)
25;. 1.00
26. 2.00
3.
h.
5;.
6.
15;.
16.
17.
18.
19.
20.
21.
22.
23.
24.
-13-
27.
28.
29.
30.
31.
3.00
400
6.00
7.00
mr+2hm -
2) Notes on output:
a) The values of line 7 are used in the equations:
log W = log a+b 
log L (1)
W = aLb (2)
b) The values of line 20 are used in the equation:
W =b 
1
+ b
2
L + b 
3
L
2 
+ b 
4
L0 (3)
c) The values in lines 1 through 6 may be used in the analysis of covariance
of two length-weight relationships as followvs: (this is presented merely to
illustrate the exact meaning of the statistical symbols in line 1 through 8)
Source
Population
Population
df
n
1
l
n
2
-1
Ex
2
Ex
2
1
Ex
2
2
Exy
Exy
1
Exy
2
Ey
2
Ey2
Ey
2
2
New
b f
~l n
1
-2
)2 
n
2
-2
Ed
2
Ed
2
1
Ed2
Edi/(n
2
-2)
Ed2 (n2-2
Within
Regression
Common
Adjusted
Means
Total
Where Exi
ExyT
j~uT
n +n -2 Ex
2
+Ex
2
1 2 1 2
n +n
2
-1lE21 2 EXT
Exy
1
+Exy 
2
EXYT
Ey2j+Ey2
2
EyT
'e ~a t T
- n +n -14 Ed
2
+Ed
2
1 2 1 2
- 1
n1n-3
1
n
1
+n
2
-2
(EX+EX) - (EX
1
+EX
2
)
2
/(n
1
+n
2
)
_ (ExY +EXY
2
) -(EX +EX 2) )(EY +
2
w.. . ..
rr u~ u~~u u7~ U(~U \1
-1h-
Ey T= (EY +EY2) - (EY
1
+EY
2
)
2
/(n+n
2
)
Subscripts 1 and 2 refer to the 
population.
d) Lines 9 through 11 form X'X matrix or A matrix and G matrix of Hader
and Grandage (1958) as follows:
Hader and Grandage Symbols
X'X =A G
a a a a g
00 01 02 03 0
all 12 a13 gl
1
a22 a23 g2
a
33  
g
3
or in our symbols
X'X = A G
n EX EX
2 
EX
3  
EY
EX
2  
EX
3 
EX4 EXY
EX4 EX5 EX
2
y
EX
6  
EX
3
Y
e) Lines 12 through 19 are Hader and Grandage (1958) symbols for the Forward
Abbreviated Doolittle solution of the X'X matrix or a matrix.
f) Lines 21 through 2h are Hader and Grandage's symbols for the inverse
X'X or C matrix.
Note: A test of the accuracy of the computations would be to calculate
the identity matrix, I, by AC = I which should be:
The degree with which the diagonal values approach unity would give a check
on the accuracy.
-15-
g) Lines 25 through m + 24 are in tabular form and are the values of weight
determined from equations (2) and (3) at integer intervals of length 1 to M.
Weights under the heading WTl are derived from equation (2). Weights under
the heading WT2 are derived from equation (3) and have a factor of 1000.0
added to each weight. If the option is taken to delete computation of equa-
tion (3), then all values under WT2 will be numerically equal to 1000.0 and
lines 9 through 24 will be deleted from the output. When observational values
are missing from either end or the middle of the range over which the output
is computed, then equation (3) often gives negative values for these missing
values. These must be disregarded and only the section of the calculated
curve which fits the empirical data should be used.
h) Line m + 24, the value of m is the value typed into columns 1 and 2 of
the header card.
i) Occasionally the answers are too large to be printed in the allotted
space. In this case the space where the answer should be is blank and the
next line has the caption: ERROR F8, which is followed by the answer in
exponential form.
j) The author found that for some species of fish a single length-weight
equation failed to adequately describe the length-weight relationship over
the entire range in length; therefore, it was necessary to compute two or
more equations for some species. The point (or points) chosen for separation
of data were those where the increment of increase or decrease in the condi-
tion index changed in magnitude.
Program II
This program is useful where fish are grouped in class intervals according to
length. The program computes average empirical weight, maximum and minimum weights,
condition index, and number of fish for each interval. The results of these comn-
putations are printed in tabular form. The condition index is computed from the
average empirical weight for each interval by the formula,
C = WX10
5  
(4)
L
3
Data cards are processed at the rate of 120 per minute, with punch out
requiring an additional minute. Accuracy is limited only by the accuracy 
of the
of the data; 5
4
70 storage positions are utilized.
Restrictions: Number of size intervals must be equal to or less than 99.
The class mark of each interval must be an integer. Input and output are on cards
with one data card required for each observation.
Card Format
1) Header Card
a. Same as for (a) under Program I.
b. All other spaces are blank or same header card 
as used for Program I may
be used.
2) Data Cards
a. Decimal point must be in column 5. A two-digit 
length would be typed
in columns 3 and 4 with the decimal in column 
. A one digit length
would be typed in column 4 with the decimal 
in column 5. The maxi-
mum length that may be entered is the two-digit number 99.
b. Same as for (b) under Program I.
c. I " 
" " (c) 
" " 
"
d. " 
, ,I (d) 
" " 
"
e. " " 
" (e) " 
" "
3) Trailer Card - same as for Program I
1) Additional notes
For data in units other than inch-groups and pounds, 
data cards should
be typed in same units of measure as field data and 
used with Program I first.
Then Program III may be used to transform these 
data cards to data cards in inch-
groups and pounds which may be used with Program 
II.
-.17-
Source Proga
DIMENS*IONW(99) ,F( 99) ,A( 99) ,C( 99) ,SI( 99) ,BI( 99) ,SM(99) ,AV(99) ,B(99) ,S(99)
16 READ 139LEVJ
13 FORMAT(12)
DO 15 J=1#99
W(J)0O
F(J)=0
A(J)=0
SI (J)=0
AV (J)=O.
B! (J)=O
SM(J)=100000*
C(J)=O
B(J)=0
S(J)=O
15 CONTINUE
2 READ 99,JFNOTOTWTPBNO
99 FORMAT(l49lXF8.QF1O.5,F4.O)
IF( J-8888)20, 14,14
20 IF(J)21,2921
21 IF(FNO)22.92922
22 IF(TOTWT)23,2,23
23 W(J)=W(J)+TOTWT
F.(J)=F(J)+FNO
AV (J )=TOTWT/FNO
I F (AV (J) -SM (-J)) 80, 80, 81
80 SM(J)=Q
SMtJ)=AV(J)'
GO TO 83
81 IF(AV(J)-BI(J) )83982v82
82 BI(J)=O
81 (J)=AV( J)
GO TO 83
83 AV(J)=0
GO TO 2
14 PUNCH 6,PBNO
6 FORMAT (5HPBNOtF8.0)
PUNCH 9
9FORMAT(4HLENG93X,7HNO FISH,4X,6HAVG WT, 5X, 3HC F,6X,5HMAXWT,7Xq5HMINWT)
DO 7 J1,tLEVJ
IF(W(J) )11,8,1
11 A(J)=W(J)/F(J)
_4 FORMATI(4X )
GO TO 16
END
-18-
Sequence of cards through the IBM 1620 is the same as for Program I
when all data are in the same units. If the cards for an inch-group are arranged
so that average weights for fish of that inch-group are in descending order for
maximum to minimum, then no maximum weight is computed. Where a great deal of
data for each inch-group is processed, it is highly unlikely that the cards would
be arranged in such an order. However, to avoid this computational error, it is
necessary only to place one data card for each inch-group ahead of one that has a
weight of greater magnitude.
Output
The output is in tabular form. The first column of the table is the length
integers from 1 to m (where m is same as in Program I). The second 
column is the
total number of fish for each length-group (length integer). The third column is
the average weight for each length-group. Column four is a condition 
index derived
from the following equation:
c - wxo
5  
(4)
L
3
where W is equal to the average weight and L is the length-integer 
for the same
length-group. Column five is the maximum weight for each length-group, 
and column
six is the minimum weight.
PROGRAM III
Title: Program to Transform Data to Inch-Groups and Pounds.
This program is used to make new data cards from data 
cards in units other
than inch-groups and pounds. The program transforms millimeters-grams, 
inches-
grams, millimeters-pounds, and inches-ounces to inch-groups arid pounds. Then these
new data cards may be used with Program II.
This program utilizes the same header card, subheader card, and data cards
as Program I. No trailer card is used. However, the data cards must have columns
1, 6, lh, 28, and 31 blank.
-19-
Source Program
1 READ 29LSET
2 FORMAT(4X~iP2)
4 READ 99#SIZEFNO*TOTWT*K*I#KI
99 FORMAT( lXF4.O,1X9F7.0,lXF9.595X911,2X,12,38XI1)
IF(KI-1 )7'7'l
7 IF(LSET-l)l1059105ol00
100 IF(LSET-3) 10691079101
101 IF(LSET-5)10891099105
105 WYz=TOTWT
WX=SIZE
GO TO 6.
106 WX=SIZE/25.4
WY=TOTWT/453. 59
GO TO 6
107 WX=SIZE/25.4
WV=TOTWT
GO TO 6
108 WY=TOTWT/453*59
WX =S IZ E
GO TO 6
109 WY=TOTWT/16*0
WX=S IZE
6 WXL=lo5
DO 70 J =199
IF(WX-WXL)65966966
65 X=WXL-*5
GO TO 88
66 WXLuWXL+1.
70 CONTINUE
88 PUNCH 39X9F'NO.WYgKgI
3 FORMAT(FS.0,tF8.0,F1O.5,4X,12,1X.13)
Wx30
F NO =0
K=O
Iw0
K1=0
GO TO 4
END
Data cards of different units can be placed in sequence through the IBM 1620,