Statistics Programs

Sample data
Have these files ready beforehand to run the following sample programs.
ex1.txt data1.txt data2.txt data3.txt data4.txt
Right click to save these.
(These are generated by using random numbers.)

　　Descriptive Statistics

Read a file to calculate the number of items, the mean and the standard deviation.

100 OPEN #1: NAME "ex1.txt"
110 LET n=0   ! Number of items
120 LET s=0   ! Sum
130 LET s2=0  ! Sum of Square 
140 DO
150    INPUT #1,IF MISSING THEN EXIT DO : x
160    LET n=n+1
170    LET s=s+x
180    LET s2=s2+x^2
190 LOOP
200 PRINT "Number of items",n
210 PRINT "Mean",s/n
220 PRINT "Standard deviation",SQR(s2/n-(s/n)^2) 
230 CLOSE #1
240 END

Make a distribution table from a test result of full mark 10 point.

120 DIM f(0 TO 10)
130 MAT f=ZER
140 OPEN #1: NAME "data2.txt"
150 DO
160    INPUT #1,IF MISSING THEN EXIT DO : x
170    LET f(x)=f(x)+1
180 LOOP
190 CLOSE #1
200 FOR x=0 TO 10
210    PRINT x;"point", f(x);"persons"
220 NEXT x
230 END

Make a class width 10 distribution table of a test result with full mark 100 point.

110 DIM f(0 TO 10)
120 MAT f=ZER
130 OPEN #1: NAME "data3.txt"
140 DO
150    INPUT #1,IF MISSING THEN EXIT DO : x
160    LET i=INT(x/10)
170    LET f(i)=f(i)+1
180 LOOP
190 CLOSE #1
200 FOR i=0 TO 10
210    PRINT i*10;"s point",f(i);"persons"
220 NEXT i
230 END

Read bivariate data to sum up the means, the standard deviations and the correlation.

100 OPEN #1:NAME "data4.txt"
110 LET n=0   ! number of items
120 LET mx=0  ! sum of x
130 LET my=0  ! sum of y 
140 LET xx=0  ! sum of x^2
150 LET yy=0  ! sum of y^2
160 LET xy=0  ! sum of x*y
170 DO
180    INPUT #1,IF MISSING THEN EXIT DO:x,y
190    LET n=n+1
200    LET mx=mx+x
210    LET my=my+y
220    LET xx=xx+x^2
230    LET yy=yy+y^2
240    LET xy=xy+x*y
250 LOOP
260 LET mx=mx/n            ! mean of x
270 LET my=my/n            ! mean of y
280 LET sx=SQR(xx/n-mx^2)  ! sd of x
290 LET sy=SQR(yy/n-my^2)  ! sd of y
300 LET sxy=xy/n-mx*my
310 PRINT sxy/(sx*sy)      ! correlation
320 CLOSE #1
330 END

PLot a scatter graph

110 OPEN #1:NAME "data4.txt"
120 SET WINDOW 100,200,0,100
130 DRAW grid WITH SCALE(10,10)
140 DO
150    INPUT #1,IF MISSING THEN EXIT DO: x,y
160    PLOT POINTS:x,y
170 LOOP
180 CLOSE #1
190 END

Plot two regression lines.

100 OPEN #1:NAME "data4.txt"
110 ! preparation
120 LET n=0   ! Number of Items
130 LET mx=0  ! Sum of x
140 LET my=0  ! Sum of y 
150 LET xx=0  ! Sum of x^2
160 LET yy=0  ! Sum of y^2
170 LET xy=0  ! Sum of x*y
180 ! Coordinate setting
190 LET left=100
200 LET right=200
210 LET bottom=0
220 LET top=100
230 SET WINDOW left,right,bottom,top
240 DRAW grid WITH SCALE(10,10) 
250 ! Read data 
260 DO
270    INPUT #1,IF MISSING THEN EXIT DO: x,y
280    LET n=n+1
290    LET mx=mx+x
300    LET my=my+y
310    LET xx=xx+x^2
320    LET yy=yy+y^2
330    LET xy=xy+x*y
340    PLOT POINTS:x,y
350 LOOP
360 ! make a suumury
370 LET mx=mx/n            ! mean of x
380 LET my=my/n            ! mean of y
390 LET sx=SQR(xx/n-mx^2)  ! sd of x
400 LET sy=SQR(yy/n-my^2)  ! sd of y
410 LET sxy=xy/n-mx*my
420 LET r=sxy/(sx*sy)      ! correlation
430 ! draw regression lines
440 DEF f(x)=a*(x-mx)+my
450 SET LINE STYLE 2
460 LET a=r*sy/sx
470 PLOT LINES:left,f(left);right,f(right)
480 SET LINE STYLE 3
490 LET a=1/r*sy/sx
500 PLOT LINES:left,f(left);right,f(right)
510 
520 CLOSE #1
530 END

Probabilities

Probability distribution of the number of dice with spot 1 rolling n dice.

110 OPTION ARITHMETIC NATIVE 
120 SET WINDOW -1,49,-0.01,0.49
130 DRAW axes0
140 INPUT n
150 FOR k=0 TO n
160    LET p=Comb(n,k)/6^n*5^(n-k)
170    PLOT LINES: k-0.5,0 ; k-0.5,p ; k+0.5,p ; k+0.5,0
180 NEXT k
190 END

A simulation of a distribution of sample means.

100 DIM a(1000)  ! population
110 LET n=10     ! sample size
120 DIM s(n)     ! sample
130 OPEN #1: NAME "data3.txt"
140 FOR i=1 TO 1000
150    INPUT #1:a(i)
160 NEXT i
170 CLOSE #1
180 DIM d(0 TO 100)
190 MAT d=ZER 
200 RANDOMIZE
210 LET times=2000  ! number of experiment
220 FOR t=1 TO times
230    FOR i=1 TO n
240       LET s(i)=a(INT(RND*1000)+1)
250    NEXT i
260    LET m=0
270    FOR i=1 TO n
280       LET m=m+s(i)
290    NEXT i
300    LET m=m/n
310    LET i=INT(m)
320    LET d(i)=d(i)+1
330 NEXT t
340 SET WINDOW 0,100,0,0.4
350 FOR i=0 TO 100
360    PLOT AREA:i,0;i+1,0;i+1,d(i)/times;i,d(i)/times
370 NEXT i
380 END

Distributions of the averages of k dice and the normal distributions approximating them.

100 DIM f(10,60)
110 MAT f=ZER
120 FOR x=1 TO 6
130    LET f(1,x)=1
140 NEXT x
150 FOR k=2 TO 10
160    FOR x=k TO 6*k
170       FOR y=x-6 TO x-1
180          IF k-1<=y AND y<=6*(k-1) THEN LET f(k,x)=f(k,x)+f(k-1,y)
190       NEXT y
200    NEXT x
210 NEXT k
220 SET WINDOW -1, 7, -0.03, 1
230 FOR k=1 TO 10
240    CLEAR
250    SET LINE COLOR 1
260    DRAW axes
270    LET w=1/k
280    FOR x=k TO 6*k
290       LET h=f(k,x)/6^k/w
300       PLOT LINES: x/k-w/2,0; x/k-w/2,h; x/k+w/2,h; x/k+w/2,0
310    NEXT x
320    WAIT DELAY 1
330    LET m=7/2
340    LET s2=35/12/k
350    LET s=SQR(s2)
360    SET LINE COLOR 4
370    FOR x=0 TO 7 STEP 0.01
380       PLOT LINES:x,1/(SQR(2*PI)*s)*EXP(-(x-m)^2/(2*s2));
390    NEXT x
400    PLOT LINES
410    WAIT DELAY 1
420 NEXT k     
430 END

Cumulative distribution of a binomial distribution B(n, p).

100 OPTION ARITHMETIC NATIVE
110 DECLARE EXTERNAL FUNCTION C
120 LET n=180
130 LET p=1/6
140 LET t=0
150 FOR k=0 TO n
160    LET t=t+C(n,k)*p^k*(1-p)^(n-k)
170    PRINT USING "###  #.######":k,t
180 NEXT k
190 END
200 ! the binomial coefficient
210 EXTERNAL FUNCTION C(n,r)
220 OPTION ARITHMETIC NATIVE
230 IF r=0 THEN LET C=1 ELSE LET C=C(n-1,r-1)*n/r
240 END FUNCTION

This program can be applied for at most n=1020. If n exceeds 1020, an overflow will occur in calculation of the binomial coefficient.

Cumulative distribution of a binomial distribution B(n, p), revised.

100 OPTION ARITHMETIC NATIVE
110 LET n=1200
120 LET p=1/6
130 LET t = (1-p)^n       !  Cumulative probability
140 LET u = 0             !  Logarithm of the binomial coefficient             
150 FOR k = 1 TO n
160    LET u = u + LOG2(n-k+1)-LOG2(k)
170    LET t = t + 2^( u + k*LOG2(p) + (n-k)*LOG2(1-p))
180    PRINT USING "#####  #.######":k,t
190 NEXT k
200 END

Overflow is suppressed using logarithm.

More sample programs are put to the public here (in Japanese).

Decimal BASIC has a library of calculating some probability distributions.
PROBDIST.LIB has normal, t, χ²，F distributions,
DiscDist.LIB has binomial, hyper-geometric, Poisson, negative binomial distributions.
These files are located in the subfolder "Library.

Example of usage.
Cumulative distribution Pr(X ≤ i), where X is the number of inferior goods sampling 6 without replacement from the bulk of 18000 goods which contains 3000 inferior goods.

10 DECLARE EXTERNAL FUNCTION HyperGeomLCum
20 DECLARE NUMERIC NN,M,n,i
30 LET NN=18000
40 LET M=3000
50 LET n=6
60 FOR i=0 TO n 
70    PRINT i,HyperGeomLCum(NN,M,n,i)
80 NEXT i
90 END
100 MERGE "discdist.lib"

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