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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: Sun, 18 Nov 2007 15:18:50 -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/Nov/18/t1195423979zfnmwpikowwsm9c.htm/, Retrieved Sun, 18 Nov 2007 23:12:59 +0100

User-defined keywords:

Dataseries X:

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99,5 101,6 103,9 106,6 108,3 102 93,8 91,6 97,7 94,8 98 103,8 97,8 91,2 89,3 87,5 90,4 94,2 102,2 101,3 96 90,8 93,2 90,9 91,1 90,2 94,3 96 99 103,3 113,1 112,8 112,1 107,4 111 110,5 110,8 112,4 111,5 116,2 122,5 121,3 113,9 110,7 120,8 141,1 147,4 148 158,1 165 187 190,3 182,4 168,8 151,2 120,1 112,5 106,2 107,1 108,5 106,5 108,3 125,6 124 127,2 136,9 135,8 124,3 115,4 113,6 114,4 118,4 117 116,5 115,4 113,6 117,4 116,9 116,4 111,1 110,2 118,9 131,8 130,6 138,3 148,4 148,7 144,3 152,5 162,9 167,2 166,5 185,6

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 119.156989247312 2.56874505164839 46.3872384574902 Geometric Mean 116.883038574663 Harmonic Mean 114.858077403893 Quadratic Mean 121.677629790352 Winsorized Mean ( 1 / 31 ) 119.140860215054 2.55575839502173 46.6166365518447 Winsorized Mean ( 2 / 31 ) 119.130107526882 2.544715479166 46.8147062028031 Winsorized Mean ( 3 / 31 ) 119.033333333333 2.51512643702738 47.326977912895 Winsorized Mean ( 4 / 31 ) 118.465591397849 2.36482744049903 50.0948142638477 Winsorized Mean ( 5 / 31 ) 118.384946236559 2.34445719468705 50.4956740113832 Winsorized Mean ( 6 / 31 ) 118.352688172043 2.33263910967465 50.7376763431487 Winsorized Mean ( 7 / 31 ) 118.247311827957 2.30657767865137 51.2652632176232 Winsorized Mean ( 8 / 31 ) 118.101075268817 2.2628540391682 52.1912033319789 Winsorized Mean ( 9 / 31 ) 117.791397849462 2.14588043521736 54.891873711282 Winsorized Mean ( 10 / 31 ) 117.253763440860 2.01905807492273 58.0734971901924 Winsorized Mean ( 11 / 31 ) 117.147311827957 1.98416510233843 59.0411108883498 Winsorized Mean ( 12 / 31 ) 116.837634408602 1.92338583652723 60.7458119893189 Winsorized Mean ( 13 / 31 ) 116.865591397849 1.90699512904863 61.2825851611651 Winsorized Mean ( 14 / 31 ) 116.986021505376 1.87380854549381 62.4322168808057 Winsorized Mean ( 15 / 31 ) 116.889247311828 1.85645926591379 62.963540034525 Winsorized Mean ( 16 / 31 ) 116.648387096774 1.72702687183584 67.5428906168533 Winsorized Mean ( 17 / 31 ) 116.081720430108 1.62491338010341 71.4387128886342 Winsorized Mean ( 18 / 31 ) 115.578494623656 1.5310254468164 75.4909037364393 Winsorized Mean ( 19 / 31 ) 115.496774193548 1.45985907759769 79.1150159394887 Winsorized Mean ( 20 / 31 ) 115.367741935484 1.40918077827129 81.868659943695 Winsorized Mean ( 21 / 31 ) 114.870967741935 1.22021750665462 94.1397473118283 Winsorized Mean ( 22 / 31 ) 114.658064516129 1.16917248017874 98.067707254451 Winsorized Mean ( 23 / 31 ) 113.916129032258 1.03585362431273 109.973191538369 Winsorized Mean ( 24 / 31 ) 113.554838709677 0.97275834793677 116.734889965764 Winsorized Mean ( 25 / 31 ) 113.501075268817 0.888933172246951 127.682348698858 Winsorized Mean ( 26 / 31 ) 113.556989247312 0.860530563924384 131.961599050525 Winsorized Mean ( 27 / 31 ) 113.150537634409 0.800516464391189 141.346921228487 Winsorized Mean ( 28 / 31 ) 113.481720430108 0.670053248874067 169.362241912562 Winsorized Mean ( 29 / 31 ) 113.419354838710 0.639353888124727 177.396832873539 Winsorized Mean ( 30 / 31 ) 113.225806451613 0.607483914957996 186.384863308589 Winsorized Mean ( 31 / 31 ) 112.992473118280 0.539245738704913 209.537999112704 Trimmed Mean ( 1 / 31 ) 118.723076923077 2.48009712526101 47.870333671139 Trimmed Mean ( 2 / 31 ) 118.286516853933 2.3925132155852 49.44027731316 Trimmed Mean ( 3 / 31 ) 117.835632183908 2.29749638676188 51.2887127322046 Trimmed Mean ( 4 / 31 ) 117.398823529412 2.19995447757693 53.3642058169845 Trimmed Mean ( 5 / 31 ) 117.1 2.14104412338694 54.6929410379261 Trimmed Mean ( 6 / 31 ) 116.804938271605 2.07853811194857 56.1957164028633 Trimmed Mean ( 7 / 31 ) 116.501265822785 2.0085039053765 58.0040026364531 Trimmed Mean ( 8 / 31 ) 116.2 1.9326837753574 60.1236485148802 Trimmed Mean ( 9 / 31 ) 115.905333333333 1.85347095217880 62.5342054576491 Trimmed Mean ( 10 / 31 ) 115.638356164384 1.78597469022620 64.7480374706417 Trimmed Mean ( 11 / 31 ) 115.426760563380 1.73299261725336 66.6054542957728 Trimmed Mean ( 12 / 31 ) 115.215942028986 1.67683508056654 68.7103599896407 Trimmed Mean ( 13 / 31 ) 115.215942028986 1.62186524829531 71.0391582470156 Trimmed Mean ( 14 / 31 ) 114.826153846154 1.55865492573398 73.6700291708773 Trimmed Mean ( 15 / 31 ) 114.598412698413 1.48797276164357 77.0164721105718 Trimmed Mean ( 16 / 31 ) 114.365573770492 1.40481001427492 81.409993243478 Trimmed Mean ( 17 / 31 ) 114.140677966102 1.32923148224682 85.869676945334 Trimmed Mean ( 18 / 31 ) 113.954385964912 1.25785519350044 90.5942007901503 Trimmed Mean ( 19 / 31 ) 113.801818181818 1.18943862748192 95.6769147667085 Trimmed Mean ( 20 / 31 ) 113.645283018868 1.11850955034237 101.604213378493 Trimmed Mean ( 21 / 31 ) 113.488235294118 1.03956117083717 109.169367304018 Trimmed Mean ( 22 / 31 ) 113.363265306122 0.982654385740943 115.364330481916 Trimmed Mean ( 23 / 31 ) 113.246808510638 0.921276168460804 122.923844540386 Trimmed Mean ( 24 / 31 ) 113.186666666667 0.874340155243202 129.453812669948 Trimmed Mean ( 25 / 31 ) 113.153488372093 0.828214726232708 136.623371678977 Trimmed Mean ( 26 / 31 ) 113.153488372093 0.787644777207634 143.660558219209 Trimmed Mean ( 27 / 31 ) 113.082051282051 0.740270875350136 152.757666210447 Trimmed Mean ( 28 / 31 ) 113.075675675676 0.692694670824072 163.240285277717 Trimmed Mean ( 29 / 31 ) 113.037142857143 0.663680667800053 170.318570875109 Trimmed Mean ( 30 / 31 ) 113 0.631496539014965 178.940014740638 Trimmed Mean ( 31 / 31 ) 112.977419354839 0.595443445079874 189.736607713741 Median 112.8 Midrange 138.9 Midmean - Weighted Average at Xnp 112.943478260870 Midmean - Weighted Average at X(n+1)p 113.246808510638 Midmean - Empirical Distribution Function 113.246808510638 Midmean - Empirical Distribution Function - Averaging 113.246808510638 Midmean - Empirical Distribution Function - Interpolation 113.246808510638 Midmean - Closest Observation 113.004166666667 Midmean - True Basic - Statistics Graphics Toolkit 113.246808510638 Midmean - MS Excel (old versions) 113.246808510638 Number of observations 93

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423979zfnmwpikowwsm9c/1e4i81195424324.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423979zfnmwpikowwsm9c/1e4i81195424324.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423979zfnmwpikowwsm9c/2w7jj1195424324.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423979zfnmwpikowwsm9c/2w7jj1195424324.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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