Paper statistiek: Central Tendency

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Sun, 06 Dec 2009 11:25:02 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t1260123992e48pewcf7ho7idb.htm/, Retrieved Sun, 06 Dec 2009 19:26:34 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t1260123992e48pewcf7ho7idb.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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ETP(30)

Dataseries X:

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0.0239732542744507 0.0208376482783286 0.0177020422821997 0.0145664362860704 0.000881931884234765 -0.00225367411189447 0.0046107198919763 0.0309262154901407 0.0277906094940115 0.0352039019035886 0.0320682959074594 0.0289326899113301 0.0257970839152009 0.0226614779190717 0.0195258719229424 0.0163902659268132 0.0132546599306839 0.0101190539345547 0.00698344793842546 -0.00670105646341016 -0.0098366624595394 -0.0129722684556686 -0.0266567728575043 -0.0297923788536335 -0.0329279848497627 -0.036063590845892 -0.0391991968420212 -0.0423348028381505 -0.0454704088342797 -0.0486060148304089 -0.0517416208265382 -0.0548772268226674 -0.0474639344130903 -0.0505995404092195 -0.0537351464053487 -0.056870752401478 -0.0600063583976072 0.0163091372005572 0.0126246327987216 0.00948902680259236 0.00635342080646312 0.00321781481033388 0.0100822088142047 0.0169466028180754 0.0138109968219462 0.0206753908258170 0.00699088642398134 0.0038552804278521 0.0107196744317229 0.0175840684355934 etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.91881196984674e-18 0.00366589466175856 5.23422560354277e-16 Geometric Mean NaN Harmonic Mean 0.0187083935328924 Quadratic Mean 0.028158271193301 Winsorized Mean ( 1 / 20 ) 1.96601993944038e-18 0.00364357938958537 5.39584767950976e-16 Winsorized Mean ( 2 / 20 ) 5.95661506797519e-05 0.00362522971651906 0.0164310003331174 Winsorized Mean ( 3 / 20 ) 6.98932036006572e-05 0.00360379876862028 0.0193943136362788 Winsorized Mean ( 4 / 20 ) 6.989320360065e-05 0.00355175100164989 0.0196785201350496 Winsorized Mean ( 5 / 20 ) 6.98932036006581e-05 0.00351544407354646 0.0198817566539036 Winsorized Mean ( 6 / 20 ) 0.000108557298920078 0.00344616131662755 0.0315009336319501 Winsorized Mean ( 7 / 20 ) 0.000196691903067925 0.00340864643688865 0.0577038149041534 Winsorized Mean ( 8 / 20 ) 0.000434956505786925 0.00334270123831424 0.130121262648731 Winsorized Mean ( 9 / 20 ) 0.00066270411785649 0.00320400497854996 0.206836169822811 Winsorized Mean ( 10 / 20 ) 0.00103111588351391 0.00306757029625982 0.336134394302589 Winsorized Mean ( 11 / 20 ) 0.00153509280805199 0.00293254739135604 0.523467348755155 Winsorized Mean ( 12 / 20 ) 0.00212090579559423 0.00279260138849697 0.75947315801334 Winsorized Mean ( 13 / 20 ) 0.00244987456858514 0.00260649052344393 0.939913092547193 Winsorized Mean ( 14 / 20 ) 0.00314365589542925 0.00244976950868968 1.28324558056513 Winsorized Mean ( 15 / 20 ) 0.00637406250846807 0.00174675445220455 3.64908902932719 Winsorized Mean ( 16 / 20 ) 0.00710711985325074 0.00157844172631571 4.50261782539144 Winsorized Mean ( 17 / 20 ) 0.00761343213402862 0.00136819091229201 5.56459779525544 Winsorized Mean ( 18 / 20 ) 0.00880508438998153 0.00111854248872677 7.87192661765068 Winsorized Mean ( 19 / 20 ) 0.00976066790399713 0.000951320949564355 10.2601208440400 Winsorized Mean ( 20 / 20 ) 0.0103268070068575 0.000801250934914087 12.8883556410013 Trimmed Mean ( 1 / 20 ) 0.000427628560241702 0.00359482261129129 0.118956790496011 Trimmed Mean ( 2 / 20 ) 0.000885802017643523 0.00353216289947794 0.250781756915698 Trimmed Mean ( 3 / 20 ) 0.00134482194373451 0.00346421334252345 0.388204134897446 Trimmed Mean ( 4 / 20 ) 0.00183517915147830 0.00338709567927311 0.54181497225143 Trimmed Mean ( 5 / 20 ) 0.00236476493584159 0.00330775703129659 0.714914944921042 Trimmed Mean ( 6 / 20 ) 0.00293848286890182 0.00321638288090640 0.913598591245372 Trimmed Mean ( 7 / 20 ) 0.00355368407976742 0.00311797049688716 1.13974268945625 Trimmed Mean ( 8 / 20 ) 0.00420764359470888 0.00299820404604733 1.40338800498118 Trimmed Mean ( 9 / 20 ) 0.00488133771773066 0.00285778059326085 1.70808694314802 Trimmed Mean ( 10 / 20 ) 0.00558444331770968 0.00270917001372589 2.06131150478425 Trimmed Mean ( 11 / 20 ) 0.00630338975468797 0.00254679998830168 2.47502347402292 Trimmed Mean ( 12 / 20 ) 0.00702585898902675 0.00236345265926397 2.97270984527134 Trimmed Mean ( 13 / 20 ) 0.00774717563511977 0.00214994682852141 3.60342662076335 Trimmed Mean ( 14 / 20 ) 0.00851120944279303 0.00190154063220608 4.47595454897995 Trimmed Mean ( 15 / 20 ) 0.00927800280670214 0.00158460135747680 5.85510214472851 Trimmed Mean ( 16 / 20 ) 0.00969285142073558 0.00144179411031535 6.72277085291711 Trimmed Mean ( 17 / 20 ) 0.0100657934737382 0.00129486790487574 7.77360643184999 Trimmed Mean ( 18 / 20 ) 0.0104264348472249 0.00115767711211613 9.00634100657504 Trimmed Mean ( 19 / 20 ) 0.0106720940074133 0.00106575187702013 10.0136760136447 Trimmed Mean ( 20 / 20 ) 0.0108160033921632 0.00100094066305481 10.8058387388853 Median 0.0104193641831388 Midrange -0.0124012282470093 Midmean - Weighted Average at Xnp 0.00811881649495355 Midmean - Weighted Average at X(n+1)p 0.00927800280670214 Midmean - Empirical Distribution Function 0.00811881649495355 Midmean - Empirical Distribution Function - Averaging 0.00927800280670214 Midmean - Empirical Distribution Function - Interpolation 0.00927800280670214 Midmean - Closest Observation 0.00811881649495355 Midmean - True Basic - Statistics Graphics Toolkit 0.00927800280670214 Midmean - MS Excel (old versions) 0.00851120944279303 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260123992e48pewcf7ho7idb/1oyu11260123901.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260123992e48pewcf7ho7idb/1oyu11260123901.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260123992e48pewcf7ho7idb/2t1ur1260123901.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260123992e48pewcf7ho7idb/2t1ur1260123901.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')

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Software written by Ed van Stee & Patrick Wessa

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