Precise Calculator
- Examples:
- Basics
- Statistics
- 2D Geometry
- 3D Geometry
- Algebra
- Programming
x=(25, 24, 23, 22, 20, 18, 17, 16, 14, 10, 8); print "mean=", ave x, " (x-mean)=", listfor(i,0,count x-1, x[i]-Ans), " Sum(x-mean)^2=", sumq Ans, " Variance=", var x, " Standard Deviation=", stdev x
Data=(14,13,12,11,10,9,8,7,6,5); Freq=(1,2,3,3,5,3,2,1,2,1); print "n=",n=sum Freq, " sum x=", s=sum(Data*Freq), " sum x^2=", s2=sumfor(i,0,count Data-1,Data[i]^2 * Freq[i]), " mean=", s/n, " variance=", (s2-s^2/n)/(n-1), " standard deviation=", sqrt Ans
X=(4,7,3); Y=(5,1,6); ave X \ /* (4+7+3)/3 */ ave Y \ /* (5+1+6)/3 */ X*Y \ /* 4*5 + 7*1 + 3*6 */ sumq(X-Y) /* (4-5)^2 + (7-1)^2 + (3-6)^2 */
B=(4,5\7,1\3,6); avex B \ /* (4+7+3)/3 */ avey B \ /* (5+1+6)/3 */ sumxy B \ /* 4*5 + 7*1 + 3*6 */ sumq(B[][0]-B[][1]) /* (4-5)^2 + (7-1)^2 + (3-6)^2 */
x=(10, 9, 9, 8, 7, 7, 7, 6, 6, 5, 3, 2); y=(14, 13, 13, 13, 12, 12, 10, 8, 8, 7, 7, 5, 5); n1=count x; n2=count y; print"Student t =",(ave(x)-ave(y))/ sqrt(((n1-1)*var(x)+(n2-1)*var(y))/(n1+n2-2)*(1/n1+1/n2))
Data1=(10, 9, 8, 7, 6, 5, 3, 2); Freq1=(1, 2, 1, 3, 2, 1, 1, 1); Data2=(14, 13, 12, 10, 8, 7, 5); Freq2=(1, 3, 2, 1, 2, 2, 2); print "n1=",n1=sum Freq1, " mean1=",m1=sum(Data1*Freq1)/n1, " variance1=", v1=(sumfor(i,0,count Data1-1,Data1[i]^2 * Freq1[i]) - m1^2*n1)/(n1-1), " n2=",n2=sum Freq2, " mean2=",m2=sum(Data2*Freq2)/n2, " variance2=", v2=(sumfor(i,0,count Data2-1,Data2[i]^2 * Freq2[i]) - m2^2*n2)/(n2-1), " t =",(m1-m2)/sqrt(((n1-1)*v1+(n2-1)*v2)/(n1+n2-2)*(1/n1+1/n2))
x=(100,40,95,90,92,85,55,60,98,20); y=(0,95,5,20,30,40,50,70,0,100); /* (n*(x*y)-sum(x)*sum(y))/sqrt((n*sumq(x)-sum(x)^2)*(n*sumq(y)-sum(y)^2) */ print "Pearson r=", lrr(x',y')
X=(86,97,99,100,101,103,106,110,112,113); Y=(2,20,28,27,50,29,7,17,6,12); Rx=rowsforeach(m,X, sumforeach(j,X,j<m) + (sumforeach(j,X,j==m)+1)/2); Ry=rowsforeach(m,Y, sumforeach(j,Y,j<m) + (sumforeach(j,Y,j==m)+1)/2); print "Spearman's rho=", lrr(Rx,Ry)
L1=(12, 12, 11, 8, 7, 6, 6); L2=(24, 24, 16, 15, 14, 12, 11, 10, 9); S1=sort(L1);S2=sort(L2); n1=count L1;n2=count L2; R1=0;R2=0;i=0;j=0;o=1;t1=0;t2=0;last=0;ties=0; merge: if(i<n1, goto merge1, 0); if(j<n2, goto take2, goto addrank); merge1: if(j>=n2, goto take1, 0); if(S1[i]<S2[j], goto take1, 0); take2: b=0; item=S2[j]; j++; goto compare; take1: b=1; item=S1[i]; i++; compare: if(item==last, goto next, 0); addrank: a=t1+t2; if(a>0,ties=ties+a-1,0); a=o-(a+1)/2; R1=R1+a*t1; R2=R2+a*t2; if(o>n1+n2, goto end, 0); t1=0;t2=0; last=item; next: o++; if(b,t1++,t2++); goto merge; end: U1=R1-n1*(n1+1)/2; U2=R2-n2*(n2+1)/2; if(U1+U2==n1*n2, gotor3,0); print "error"; return; print "SUM OF RANKS 1=",R1, " SUM OF RANKS 2=",R2, " NUMBER OF TIES=",ties, " U=",U=max(U1,U2), " MEAN U=",Mu=n1*n2/2, " STD DEV U=",Su=sqrt(n1*n2*(n1+n2+1)/12), " Z=",(U-Mu)/Su
L1=(51,49,46,45,46,39,38,40,41,40,49,55,45,37,44,52,37); L2=(50,48,46,44,45,41,39,39,39,42,48,56,48,36,45,51,36); D=sort(L1-L2); n=count D; i=-1; i++; if(i==n, gotor1, if(D[i]<0, gotor-1, 0)); if(i>0,gotor3,0); print "Sum of ""-"" ranks= 0"; return; S1=listforeach(x, reverse D[0,i-1], abs x); i--; i++; if(i==n, gotor1, if(D[i]==0, gotor-1, 0)); if(i<n,gotor3,0); print "Sum of ""+"" ranks= 0"; return; S2=D[i,n-1]; n1=count S1; n2=count S2; R1=0;R2=0;i=0;j=0;o=1;t1=0;t2=0;last=0; merge: if(i<n1, goto merge1, 0); if(j<n2, goto take2, goto addrank); merge1: if(j>=n2, goto take1, 0); if(S1[i]<S2[j], goto take1, 0); take2: b=0; item=S2[j]; j++; goto compare; take1: b=1; item=S1[i]; i++; compare: if(item==last, goto next, 0); addrank: a=t1+t2; a=o-(a+1)/2; R1=R1+a*t1; R2=R2+a*t2; if(o>n1+n2, goto end, 0); t1=0;t2=0; last=item; next: o++; if(b,t1++,t2++); goto merge; end: print "Sum of ""-"" ranks=",R1, " Sum of ""+"" ranks=",R2," N=",N=n1+n2," W=",abs(R1-R2)," Normal distribution approximation: Z=",z=(abs(R1-R2)-.5)/sqrt(N*(N+1)*(2*N+1)/6)," p=",2*exp(-z^2/2)/sqrt(2*pi) * polynom(1/(1+0.2316419*z), (0,0.319381530,-0.356563782,1.781477937,-1.821255978,1.330274429))