R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 16 Apr 2008 08:03:55 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/16/t120835466827vapd6h9xw2bp6.htm/, Retrieved Wed, 16 Apr 2008 16:04:28 +0200

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Dataseries X:

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12,23 12,25 12,33 12,37 12,38 12,41 12,41 12,41 12,43 12,44 12,46 12,46 12,46 12,47 12,55 12,58 12,6 12,62 12,62 12,66 12,7 12,76 12,79 12,81 12,86 13,03 13,09 13,15 13,17 13,18 13,18 13,19 13,19 13,19 13,25 13,24 13,3 13,35 13,35 13,35 13,36 13,37 13,38 13,39 13,4 13,4 13,44 13,44 13,44 13,47 13,52 13,58 13,65 13,66 13,68 13,68 13,77 13,78 13,79 13,79 13,82 13,86 13,94 14 14,02 14,03 14,07 14,1 14,1 14,16 14,17 14,17

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 13.2041666666667 0.0682238186898074 193.5418878662 Geometric Mean 13.1916185756177 Harmonic Mean 13.1790443607943 Quadratic Mean 13.2166745481271 Winsorized Mean ( 1 / 24 ) 13.2044444444444 0.0681684971943598 193.703029814437 Winsorized Mean ( 2 / 24 ) 13.2063888888889 0.067691450385002 195.096852169310 Winsorized Mean ( 3 / 24 ) 13.2055555555556 0.0669094431840695 197.364600976080 Winsorized Mean ( 4 / 24 ) 13.2061111111111 0.066812210714873 197.660142806370 Winsorized Mean ( 5 / 24 ) 13.2061111111111 0.0660658239701339 199.893232499168 Winsorized Mean ( 6 / 24 ) 13.2027777777778 0.0654621891553218 201.685552349183 Winsorized Mean ( 7 / 24 ) 13.2018055555556 0.0652898696056112 202.202970159109 Winsorized Mean ( 8 / 24 ) 13.2018055555556 0.0645231474486931 204.605727983949 Winsorized Mean ( 9 / 24 ) 13.1955555555556 0.0630348442059813 209.337481860603 Winsorized Mean ( 10 / 24 ) 13.1872222222222 0.0607749324862627 216.984563910507 Winsorized Mean ( 11 / 24 ) 13.1811111111111 0.0598389059207966 220.276606135777 Winsorized Mean ( 12 / 24 ) 13.1761111111111 0.0590971308493948 222.956866462596 Winsorized Mean ( 13 / 24 ) 13.1779166666667 0.0587899424704664 224.152569519637 Winsorized Mean ( 14 / 24 ) 13.1915277777778 0.0559260703182782 235.874391007702 Winsorized Mean ( 15 / 24 ) 13.1956944444444 0.0546162549496907 241.607456545667 Winsorized Mean ( 16 / 24 ) 13.1801388888889 0.0510440652614745 258.210995173940 Winsorized Mean ( 17 / 24 ) 13.1848611111111 0.0502925685495662 262.163208031753 Winsorized Mean ( 18 / 24 ) 13.1798611111111 0.0496050493162389 265.69595822973 Winsorized Mean ( 19 / 24 ) 13.1877777777778 0.0475808439044508 277.165697276424 Winsorized Mean ( 20 / 24 ) 13.1794444444444 0.0432438082485165 304.770670721318 Winsorized Mean ( 21 / 24 ) 13.1794444444444 0.0382857884824355 344.23855343846 Winsorized Mean ( 22 / 24 ) 13.1733333333333 0.0350005589045472 376.374942161906 Winsorized Mean ( 23 / 24 ) 13.1701388888889 0.0328887565489766 400.445023492343 Winsorized Mean ( 24 / 24 ) 13.1868055555556 0.0303383543211275 434.657905830189 Trimmed Mean ( 1 / 24 ) 13.2042857142857 0.0673544966316577 196.041636039478 Trimmed Mean ( 2 / 24 ) 13.2041176470588 0.0663692927815623 198.949199150228 Trimmed Mean ( 3 / 24 ) 13.2028787878788 0.0654743370967011 201.649674870003 Trimmed Mean ( 4 / 24 ) 13.201875 0.0647265596935439 203.963798825489 Trimmed Mean ( 5 / 24 ) 13.2006451612903 0.0638322559479504 206.802109141408 Trimmed Mean ( 6 / 24 ) 13.1993333333333 0.0629522582384921 209.672118247580 Trimmed Mean ( 7 / 24 ) 13.1986206896552 0.062018598910004 212.817137465615 Trimmed Mean ( 8 / 24 ) 13.1980357142857 0.0608897340860399 216.75305225732 Trimmed Mean ( 9 / 24 ) 13.1974074074074 0.0596584649301226 221.216007198063 Trimmed Mean ( 10 / 24 ) 13.1976923076923 0.0584526567040613 225.784302234723 Trimmed Mean ( 11 / 24 ) 13.1992 0.0574213499368608 229.86572092982 Trimmed Mean ( 12 / 24 ) 13.2016666666667 0.056281282344282 234.565847059239 Trimmed Mean ( 13 / 24 ) 13.205 0.0549455153933035 240.328986005096 Trimmed Mean ( 14 / 24 ) 13.2084090909091 0.0532574654880735 248.010470829991 Trimmed Mean ( 15 / 24 ) 13.2104761904762 0.0517183837460137 255.430955757476 Trimmed Mean ( 16 / 24 ) 13.21225 0.0499698466770019 264.404453457745 Trimmed Mean ( 17 / 24 ) 13.2160526315789 0.0484548439515936 272.749875013152 Trimmed Mean ( 18 / 24 ) 13.2197222222222 0.0465482956418438 284.000134482659 Trimmed Mean ( 19 / 24 ) 13.2244117647059 0.044036913652943 300.302874741134 Trimmed Mean ( 20 / 24 ) 13.22875 0.041098205556934 321.881450071439 Trimmed Mean ( 21 / 24 ) 13.2346666666667 0.0382301960852977 346.183593647755 Trimmed Mean ( 22 / 24 ) 13.2414285714286 0.0357005264500862 370.902893825438 Trimmed Mean ( 23 / 24 ) 13.25 0.0329475107032149 402.154812828002 Trimmed Mean ( 24 / 24 ) 13.2604166666667 0.0292817347150524 452.856253077454 Median 13.275 Midrange 13.2 Midmean - Weighted Average at Xnp 13.2035135135135 Midmean - Weighted Average at X(n+1)p 13.2035135135135 Midmean - Empirical Distribution Function 13.2035135135135 Midmean - Empirical Distribution Function - Averaging 13.2035135135135 Midmean - Empirical Distribution Function - Interpolation 13.2035135135135 Midmean - Closest Observation 13.2035135135135 Midmean - True Basic - Statistics Graphics Toolkit 13.2035135135135 Midmean - MS Excel (old versions) 13.2279487179487 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t120835466827vapd6h9xw2bp6/1c9a91208354630.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t120835466827vapd6h9xw2bp6/1c9a91208354630.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t120835466827vapd6h9xw2bp6/2i7n91208354630.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t120835466827vapd6h9xw2bp6/2i7n91208354630.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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