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

Title produced by software: Central Tendency

Date of computation: Thu, 13 Dec 2007 03:14:58 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/13/t11975399620ddnbfjctk92sbl.htm/, Retrieved Thu, 13 Dec 2007 10:59:24 +0100

User-defined keywords:

Dataseries X:

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0.4 0.37 0.36 0.36 0.36 0.36 0.32 0.31 0.32 0.33 0.33 0.29 0.33 0.32 0.31 0.33 0.32 0.32 0.3 0.3 0.33 0.35 0.35 0.37 0.38 0.39 0.4 0.32 0.29 0.29 0.3 0.3 0.32 0.32 0.34 0.34 0.34 0.33 0.33 0.33 0.34 0.35 0.34 0.36 0.39 0.43 0.42 0.39 0.37 0.36 0.39 0.39 0.37 0.36 0.38 0.38 0.44 0.49 0.47 0.48 0.51 0.5 0.47 0.47 0.44 0.43 0.45 0.46 0.46 0.45 0.45 0.45 0.44 0.43 0.45 0.45 0.44 0.47 0.46 0.48

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.38025 0.0067925289375231 55.9806227544257 Geometric Mean 0.375574142857948 Harmonic Mean 0.371053043321124 Quadratic Mean 0.385012986793952 Winsorized Mean ( 1 / 26 ) 0.380125 0.00676339212978708 56.203306374307 Winsorized Mean ( 2 / 26 ) 0.379875 0.00670936845015982 56.6185927664997 Winsorized Mean ( 3 / 26 ) 0.379875 0.00657357037930268 57.7882304563227 Winsorized Mean ( 4 / 26 ) 0.379875 0.00657357037930268 57.7882304563227 Winsorized Mean ( 5 / 26 ) 0.37925 0.00645768848012422 58.7284445769215 Winsorized Mean ( 6 / 26 ) 0.37925 0.00645768848012422 58.7284445769215 Winsorized Mean ( 7 / 26 ) 0.380125 0.00632829128356306 60.0675574127453 Winsorized Mean ( 8 / 26 ) 0.380125 0.00632829128356306 60.0675574127453 Winsorized Mean ( 9 / 26 ) 0.380125 0.00598123053149484 63.5529759300213 Winsorized Mean ( 10 / 26 ) 0.380125 0.00598123053149484 63.5529759300213 Winsorized Mean ( 11 / 26 ) 0.380125 0.00598123053149484 63.5529759300213 Winsorized Mean ( 12 / 26 ) 0.378625 0.00573613835501273 66.0069504197236 Winsorized Mean ( 13 / 26 ) 0.378625 0.00573613835501273 66.0069504197236 Winsorized Mean ( 14 / 26 ) 0.378625 0.00573613835501273 66.0069504197236 Winsorized Mean ( 15 / 26 ) 0.378625 0.00573613835501273 66.0069504197236 Winsorized Mean ( 16 / 26 ) 0.378625 0.00573613835501273 66.0069504197236 Winsorized Mean ( 17 / 26 ) 0.38075 0.00547368561183552 69.560078345881 Winsorized Mean ( 18 / 26 ) 0.3785 0.00512223991747281 73.8934540549094 Winsorized Mean ( 19 / 26 ) 0.3785 0.00512223991747281 73.8934540549094 Winsorized Mean ( 20 / 26 ) 0.3785 0.00512223991747281 73.8934540549094 Winsorized Mean ( 21 / 26 ) 0.3785 0.00512223991747281 73.8934540549094 Winsorized Mean ( 22 / 26 ) 0.37575 0.00471254385870871 79.7340059351638 Winsorized Mean ( 23 / 26 ) 0.37575 0.00471254385870871 79.7340059351638 Winsorized Mean ( 24 / 26 ) 0.37575 0.00471254385870871 79.7340059351638 Winsorized Mean ( 25 / 26 ) 0.37575 0.00388430385728205 96.7354804891403 Winsorized Mean ( 26 / 26 ) 0.36925 0.00298612296795474 123.655322959760 Trimmed Mean ( 1 / 26 ) 0.37974358974359 0.00666243878335379 56.9976853959822 Trimmed Mean ( 2 / 26 ) 0.379342105263158 0.00654360683392922 57.9714085657214 Trimmed Mean ( 3 / 26 ) 0.379054054054054 0.00643702992638624 58.886483112384 Trimmed Mean ( 4 / 26 ) 0.37875 0.00636936101825824 59.464363680169 Trimmed Mean ( 5 / 26 ) 0.378428571428571 0.00628724336756337 60.1899034767652 Trimmed Mean ( 6 / 26 ) 0.378235294117647 0.00622218543537654 60.7881745161711 Trimmed Mean ( 7 / 26 ) 0.378030303030303 0.00614213806410986 61.5470214255251 Trimmed Mean ( 8 / 26 ) 0.37765625 0.00607387632293493 62.1771386048761 Trimmed Mean ( 9 / 26 ) 0.377258064516129 0.00598857256059593 62.9963252008401 Trimmed Mean ( 10 / 26 ) 0.376833333333333 0.00595411677676354 63.2895435984659 Trimmed Mean ( 11 / 26 ) 0.376379310344828 0.00590660460595485 63.7217717206556 Trimmed Mean ( 12 / 26 ) 0.375892857142857 0.0058430599621865 64.3315077331838 Trimmed Mean ( 13 / 26 ) 0.375555555555556 0.00580769548195218 64.6651596528469 Trimmed Mean ( 14 / 26 ) 0.375192307692308 0.0057570887814904 65.1704918809985 Trimmed Mean ( 15 / 26 ) 0.3748 0.00568736515875142 65.9004634902468 Trimmed Mean ( 16 / 26 ) 0.374375 0.00559339030203704 66.9316782459571 Trimmed Mean ( 17 / 26 ) 0.373913043478261 0.00546820640095418 68.3794677927692 Trimmed Mean ( 18 / 26 ) 0.373181818181818 0.00535003830450739 69.7531114622887 Trimmed Mean ( 19 / 26 ) 0.372619047619048 0.00526928209301673 70.7153348485313 Trimmed Mean ( 20 / 26 ) 0.372 0.00515403750123169 72.1764247759356 Trimmed Mean ( 21 / 26 ) 0.371315789473684 0.00499175782445763 74.3857780228007 Trimmed Mean ( 22 / 26 ) 0.370555555555556 0.00476335956613198 77.7929002442409 Trimmed Mean ( 23 / 26 ) 0.37 0.00456679482495788 81.0196240868809 Trimmed Mean ( 24 / 26 ) 0.369375 0.00428184228890985 86.2654378832906 Trimmed Mean ( 25 / 26 ) 0.368666666666667 0.00385761922092368 95.5684440462715 Trimmed Mean ( 26 / 26 ) 0.367857142857143 0.00353954017793298 103.927946672430 Median 0.365 Midrange 0.4 Midmean - Weighted Average at Xnp 0.372222222222222 Midmean - Weighted Average at X(n+1)p 0.372222222222222 Midmean - Empirical Distribution Function 0.372222222222222 Midmean - Empirical Distribution Function - Averaging 0.372222222222222 Midmean - Empirical Distribution Function - Interpolation 0.372222222222222 Midmean - Closest Observation 0.372222222222222 Midmean - True Basic - Statistics Graphics Toolkit 0.372222222222222 Midmean - MS Excel (old versions) 0.372222222222222 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t11975399620ddnbfjctk92sbl/1llxl1197540896.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t11975399620ddnbfjctk92sbl/1llxl1197540896.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t11975399620ddnbfjctk92sbl/2l7gn1197540896.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t11975399620ddnbfjctk92sbl/2l7gn1197540896.ps (open in new window)

Parameters:

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')

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Software written by Ed van Stee & Patrick Wessa

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