Central Tendency - Totale Productie

*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: Thu, 18 Dec 2008 06:12:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/18/t1229606105tb0ckpyfga17p3x.htm/, Retrieved Thu, 18 Dec 2008 14:15:05 +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/2008/Dec/18/t1229606105tb0ckpyfga17p3x.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

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Dataseries X:

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101,5 100,7 110,6 96,8 100,0 104,8 86,8 92,0 100,2 106,6 102,1 93,7 97,6 96,9 105,6 102,8 101,7 104,2 92,7 91,9 106,5 112,3 102,8 96,5 101,0 98,9 105,1 103,0 99,0 104,3 94,6 90,4 108,9 111,4 100,8 102,5 98,2 98,7 113,3 104,6 99,3 111,8 97,3 97,7 115,6 111,9 107,0 107,1 100,6 99,2 108,4 103,0 99,8 115,0 90,8 95,9 114,4 108,2 112,6 109,1 105,0 105,0 118,5 103,7 112,5 116,6 96,6 101,9 116,5 119,3 115,4 108,5 111,5 108,8 121,8 109,6 112,2 119,6 104,1 105,3 115,0 124,1 116,8 107,5 115,6 116,2 116,3 119,0 111,9 118,6 106,9 103,2

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 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 105.763043478261 0.844279982837578 125.270106633107 Geometric Mean 105.455546750168 Harmonic Mean 105.147296044618 Quadratic Mean 106.069255472647 Winsorized Mean ( 1 / 30 ) 105.777173913043 0.829820903058928 127.469883589486 Winsorized Mean ( 2 / 30 ) 105.738043478261 0.818535047194776 129.179616487576 Winsorized Mean ( 3 / 30 ) 105.764130434783 0.809753877068797 130.612687916525 Winsorized Mean ( 4 / 30 ) 105.755434782609 0.806562554102265 131.118701512642 Winsorized Mean ( 5 / 30 ) 105.771739130435 0.795675312115424 132.933292663341 Winsorized Mean ( 6 / 30 ) 105.830434782609 0.783077313645215 135.146853239777 Winsorized Mean ( 7 / 30 ) 105.769565217391 0.749659484939565 141.090144715394 Winsorized Mean ( 8 / 30 ) 105.865217391304 0.729092129932035 145.20142660321 Winsorized Mean ( 9 / 30 ) 105.914130434783 0.71887656806911 147.332845636165 Winsorized Mean ( 10 / 30 ) 105.903260869565 0.713817370970527 148.361843205883 Winsorized Mean ( 11 / 30 ) 105.915217391304 0.708503963418123 149.491354826478 Winsorized Mean ( 12 / 30 ) 105.85 0.694376256141559 152.438968158527 Winsorized Mean ( 13 / 30 ) 105.906521739130 0.686479215421348 154.274913733735 Winsorized Mean ( 14 / 30 ) 105.921739130435 0.675536321566612 156.796512265685 Winsorized Mean ( 15 / 30 ) 105.872826086957 0.663370160293101 159.598414918419 Winsorized Mean ( 16 / 30 ) 105.959782608696 0.651793915015138 162.566388190713 Winsorized Mean ( 17 / 30 ) 105.941304347826 0.623125286158531 170.016057285907 Winsorized Mean ( 18 / 30 ) 105.765217391304 0.586851134564001 180.224951716047 Winsorized Mean ( 19 / 30 ) 105.641304347826 0.564184574030175 187.24599928919 Winsorized Mean ( 20 / 30 ) 105.663043478261 0.555650549522945 190.160962801131 Winsorized Mean ( 21 / 30 ) 105.640217391304 0.546594066503698 193.269967358106 Winsorized Mean ( 22 / 30 ) 105.735869565217 0.528381272419652 200.112825878582 Winsorized Mean ( 23 / 30 ) 105.710869565217 0.512209869217297 206.381945991695 Winsorized Mean ( 24 / 30 ) 105.763043478261 0.505860818959992 209.075381041965 Winsorized Mean ( 25 / 30 ) 105.844565217391 0.489259618233028 216.336197129147 Winsorized Mean ( 26 / 30 ) 105.788043478261 0.474653398807774 222.874298896790 Winsorized Mean ( 27 / 30 ) 105.788043478261 0.467326729725132 226.368484294665 Winsorized Mean ( 28 / 30 ) 105.605434782609 0.428484044648106 246.462933921700 Winsorized Mean ( 29 / 30 ) 105.447826086957 0.370271520900333 284.785137756625 Winsorized Mean ( 30 / 30 ) 105.35 0.342779245411048 307.340661403430 Trimmed Mean ( 1 / 30 ) 105.77 0.81126502225203 130.3766304461 Trimmed Mean ( 2 / 30 ) 105.7625 0.790039403042314 133.869905213241 Trimmed Mean ( 3 / 30 ) 105.775581395349 0.772582387810445 136.911717202258 Trimmed Mean ( 4 / 30 ) 105.779761904762 0.756287054182771 139.867212217543 Trimmed Mean ( 5 / 30 ) 105.786585365854 0.73856995825945 143.231638631979 Trimmed Mean ( 6 / 30 ) 105.79 0.72124979433119 146.675951704220 Trimmed Mean ( 7 / 30 ) 105.782051282051 0.704388374632083 150.175748339548 Trimmed Mean ( 8 / 30 ) 105.784210526316 0.69250638766217 152.755573682767 Trimmed Mean ( 9 / 30 ) 105.771621621622 0.68284506276991 154.898420430203 Trimmed Mean ( 10 / 30 ) 105.751388888889 0.673343888076631 157.054056272734 Trimmed Mean ( 11 / 30 ) 105.731428571429 0.662933261139633 159.490305841146 Trimmed Mean ( 12 / 30 ) 105.708823529412 0.65141412760687 162.275914889594 Trimmed Mean ( 13 / 30 ) 105.708823529412 0.640120583796378 165.138922579996 Trimmed Mean ( 14 / 30 ) 105.66875 0.627814594983745 168.312031679888 Trimmed Mean ( 15 / 30 ) 105.641935483871 0.614768654973994 171.840146092581 Trimmed Mean ( 16 / 30 ) 105.618333333333 0.601008999371723 175.735028000818 Trimmed Mean ( 17 / 30 ) 105.584482758621 0.586079707564167 180.153793751784 Trimmed Mean ( 18 / 30 ) 105.55 0.572758193352088 184.283701612830 Trimmed Mean ( 19 / 30 ) 105.529629629630 0.562667039439885 187.552535038627 Trimmed Mean ( 20 / 30 ) 105.519230769231 0.553836465056866 190.524166295905 Trimmed Mean ( 21 / 30 ) 105.506 0.543904328321946 193.978967450962 Trimmed Mean ( 22 / 30 ) 105.49375 0.532668631524927 198.047611134885 Trimmed Mean ( 23 / 30 ) 105.471739130435 0.521375577845475 202.295127758543 Trimmed Mean ( 24 / 30 ) 105.45 0.509637561385177 206.91175060447 Trimmed Mean ( 25 / 30 ) 105.421428571429 0.495162847182419 212.902541398853 Trimmed Mean ( 26 / 30 ) 105.421428571429 0.479193867678326 219.99744922069 Trimmed Mean ( 27 / 30 ) 105.344736842105 0.461007267655321 228.509926487467 Trimmed Mean ( 28 / 30 ) 105.302777777778 0.437733812553425 240.563499455335 Trimmed Mean ( 29 / 30 ) 105.273529411765 0.416703573913292 252.634092919179 Trimmed Mean ( 30 / 30 ) 105.25625 0.403935715801413 260.576735065802 Median 105 Midrange 105.45 Midmean - Weighted Average at Xnp 105.351063829787 Midmean - Weighted Average at X(n+1)p 105.471739130435 Midmean - Empirical Distribution Function 105.351063829787 Midmean - Empirical Distribution Function - Averaging 105.471739130435 Midmean - Empirical Distribution Function - Interpolation 105.471739130435 Midmean - Closest Observation 105.351063829787 Midmean - True Basic - Statistics Graphics Toolkit 105.471739130435 Midmean - MS Excel (old versions) 105.49375 Number of observations 92

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229606105tb0ckpyfga17p3x/12emb1229605963.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229606105tb0ckpyfga17p3x/12emb1229605963.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229606105tb0ckpyfga17p3x/2wx8v1229605963.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229606105tb0ckpyfga17p3x/2wx8v1229605963.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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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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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