Standard Deviation
 
 x=(25,24,23,22,20,18,17,16,14,10,8);
 print"n=",count(x);print"sum x=",
 sum(x);print"sum x^2=",sumq(x);
 print"mean=",ave(x);print"var=",
 var(x);print"Stan Dev=",stdev(x)

 print   print to screen items between parenthese (" ")
 count   (n=) number of items in list
 sum   (Σx) sum of values
 sumq   (Σx²) sum of squared values
 ave   (x̄ ) average, mean
 var   variance
 stdev   standard deviation
fig. 1  Standard Deviation fig. 2  Standard Deviation
     reference: AJ Design    Standard Deviation      reference: Wolfram MathWorld    Standard Deviation
  Standard Deviation with Frequency List
 
 x=(14,13,12,11,10,9,8,7,6,5);
 y=(1,2,3,3,5,3,2,1,2,1);
 print"n=",sum(y);n=sum(y);
b=(listfor(i,0,count x-1,(x[i]
 *y[i]);print"sumx=",w=sum(b);
print"mean=",sum
 (b)/sum(y);print"sumx^2=",
z=sumfor(i,0,count x-1,x[i]*x
 [i]*y[i]);print"SD=",sqrt((z-(w^2)/n)/(n-1)


 There should be assignments to variables at the beginning of a formula.  Example: volume of a cylinder can be written as r=1;v=2;v*pi*r^2.  Then you can use keyboard shortcuts Ctrl+1 and Ctrl+2 to easily  change values of variables r, v.
fig. 3  Standard Deviation with Frequency List fig. 4  Standard Deviation
     reference: AJ Design    Standard Deviation      reference: Wolfram MathWorld    Standard Deviation
  fig. 5   Wilcoxen Matched-Pairs Signed-Ranks Test
     Sum of "-" ranks= 63.5
     Sum of "+" ranks= 72.5
     N= 16
     W= 9
     normal distribution approximation
     z= 0.2197622682 98
     p= 0.8260563772 92

 Wilcoxen Matched-Pairs Signed-Ranks Test
 



   reference: AJ Design    Standard Deviation
   reference: Wolfram MathWorld    Standard Deviation
Wilcoxen Matched Pairs
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 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 if(j merge1: if(j>=n2, goto take1, 0);
if(S1[i] 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)
   x=(25, 24, 23, 22, 20, 18, 17, 16, 14, 10, 8);
 print"x-ave=",listfor(i,0,count x-1,(x[i]-ave x);print"";
 print" S(x-ave)^2=", sumfor(i,0,count x-1,(x[i]-ave x)^
 2);print"variance=",var x;print"Standard Deviation",stdev x

 listfor(x,a,b,f(x))   values f(x) where x is from a to b.
 sumfor(x,a,b,f(x))
   for(variable,start,end[,step],function)
fig. 7  Sum of Squares fig. 8  Sum of Squares commands
     reference: AJ Design    Standard Deviation      reference: Wolfram MathWorld    Standard Deviation
   
fig. 9  Student 't' test fig. 10  PrecCalc 't' test commands
Reference:
   Handbook of Biological Statistics     Student t Test
Reference:
   Handbook of Biological Statistics    Student t Test
   
fig. 11  Student t test fig. 12  Pearson r
  print"t =",(ave(x)-ave(y))/sqrt((((n1-1)*var(x)+    print" Pearson r";x=(100,40,95,90,92,85,55,60,98,20)
  (n2-1)*var(y))/((n1+n2)-2)*(1/n1+1/n2))   ;y=(0,95,5,20,30,40,50,70,0,100);print"n=10";n=10;
     print" sumx=",sum(x);print" sumx^2=",sumq(x);print
     " sumy=", sum(y); print" sumy^2=",sumq(y); print
     " sumxy=",sum(x*y);print"r=",(n*sum(x)*sum(y))-
     sum(x)*sum(y))/sqrt((n*sumq(x)-sum(x)^2)*(n*
     sumq(y)-sum(y)^2)
     reference: Wikipedia    Student's t-test      reference: Wikipedia    Pearson r
 
Reference:
   √ = sqrt
   x² (or exponent 2) = ^2
   π = pi
 
Statistics Programs (Macros) copy and paste program (macro) into "Precise Calculator"
 
Standard Deviation
  x=(25,24,23,22,20,18,17,16,14,10,8);
  print"n=",count(x);print"sum x=",
  sum(x);print"sum x^2=",sumq(x);
  print"mean=",ave(x);print"var=",
  var(x);print"Stan Dev=",stdev(x)

You may change the list (x=) to any number. Be sure and place commas (,) between numbers.
 
Standard Deviation with Frequency List
  x=(14,13,12,11,10,9,8,7,6,5); y=(1,2,3,3,5,3,2,1,2,1);
  print"n=",sum(y);n=sum(y);b=(listfor(i,0,count x-1,(x[i]
  *y[i]);print"sumx=",w=sum(b);print"mean=",sum
  (b)/sum(y);print"sumx^2=",z=sumfor(i,0,count x-1,x[i]*x
  [i]*y[i]);print"SD=",sqrt((z-(w^2)/n)/(n-1)
 
Standard Deviation with Frequency List
  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;
  print"sum x=",s=sum (Data*Freq);
  print "sum x^2=", s2=sumfor(i,0,count Data-1,Data[i]^2 * Freq[i]);
  print"mean=",s/n;
  print "variance=", v=(s2 -s^2/n)/(n-1);
  print "standard deviation=", sqrt v;
 
Standard Deviation sum of squares
  x=(25, 24, 23, 22, 20, 18, 17, 16, 14, 10, 8);
  print"x-ave=",listfor(i,0,count x-1,(x[i]-ave x);print"";
  print" S(x-ave)^2=", sumfor(i,0,count x-1,(x[i]-ave x)^
  2);print"variance=",var x;print"Standard Deviation",stdev x
 
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Documentation & Tutorial
   Designed for the new user Maxima by Example is a series of tutorial notes which include many examples of the power of Maxima.
 
Free Math eBooks:
GraphPad QuickCalcs: free statistical calculators
   QuickCalcs: Dozens of free online calculators for Gaussian distribution, Fisher's, Chi square, McNemar's, Sign test, CI of proportion, t tests, ANOVA post tests, and much more.
free Statistics books
   This section contains free e-books and guides on Statistics, some of the resources in this section can be viewed online and some of them can be downloadable.
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   A large collection of links to interactive web pages that perform statistical calculations
Elementary statistics Download books for free
   In these free books you find an overview of elementary concepts in statistics. They cover subjects as sampling, probability, distribution and population interpretations.
HyperStat Online Statistics Textbook
   An introductory-level textbook in statistics covering descriptive and inferential statistics.
 
Statistical References and Formulas:
   Electronic Statistics Textbook
statsoft textbook
  This Textbook offers training in the understanding and application of statistics. StatSoft has freely provided the Electronic Statistics Textbook as a public service.
 
 
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