.Open Statistics . Also See .See ./math_81_Probabillity.html . Online Statistics and Probability Calculators .See http://easycalculation.com/statistics/statistics.php .See http://statpages.org/ .See ../tools/stats.scm (Local Scheme functions) . Notes and definitions on statistics. STATISTICS::=following, .Net . Definition of a (finite) sample I :: Finite_Sets=given. `I` standards for index. Typically it is a range 1..`n` where `n` is the sample size. However in some languages/cultures `I` could be 0..`n`-1. In fact there is no reason to limit `I` to a range. Any finite set of indices will work. Sample::=I>->Real. Each index item has a measured value. Example. For example the list (1,2,3) has `I` = 1..3 and size=3. size::Real= |I|. n:=size. Local shorthand. For p:Real, p::Sample = I +> p. A coercion that converts a single value into a sample with the same value for each index. This turns out to be useful when we subtract the mean of a sample (a number) from every item in the sample. For x,y::\$Sample I will use `x` and `y` as the names of samples of data. . Statistics on one sample mean(x)::= +x/n. In \$STANDARD (+) is a serial operator that adds up all the items in its arguments. +(1,2,3) = (1+2+3) = 6. mean((1, 2, 3)) = +(1, 2, 3)/3 = 6/3 = 2. min, max, range, mode, histogram are to be done. .Hole stats1 ss(x)::=+(x*x). Sum of squares. ss((1, 2, 3)) = +(1*1, 2*2 , 3*3) = +(1,4,9) = 14. ms(x) ::= ss(x - mean(x) )/n. Mean squares about mean. (-1)|- ms(x) =( ss(x) - (+x)*mean(x))/n. Better for small hand calculations. ms((1,2,3)) = (14 - 6*2)/3 = 2/3. var(x)::= n * ms(x)/(n-1). Sample variance -- rescale to allow for estimating the mean. root_mean_square(x)::=sqrt(ms(x)). rms ::= root_mean_square. standard_deviation(x)::=sqrt( var (x) ). sd(x)::=standard_deviation(x). . Statistics on Two samples SP(x,y)::=+((x-mean(x))*(y-mean(y))). (-1)|- ss(x) = SP(x,x). MS(x,y)::=SP(x,y)/n. r(x,y)::= MS(x,y)/( sd(x)*sd(y)). Correlation coefficient -- Pearson. More... .Hole stats2 .Close.Net STATISTICS .Close Statistics in MATHS