*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 20 Oct 2010 15:30:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Oct/20/t1287588585bmev3kuf0z6suxe.htm/, Retrieved Wed, 20 Oct 2010 17:29:48 +0200

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/2010/Oct/20/t1287588585bmev3kuf0z6suxe.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

84,9 81,9 95,9 81 89,2 102,5 89,8 88,8 83,2 90,2 100,4 187,1 87,6 85,4 86,1 86,7 89,1 103,7 86,9 85,2 80,8 91,2 102,8 182,5 80,9 83,1 88,3 86,6 93 105,3 93,8 86,4 87 96,7 100,5 196,7 86,8 88,2 93,8 85 90,4 115,9 94,9 87,7 91,7 95,9 106,8 204,5 90,2 90,5 93,2 97,8 99,4 120 108,2 98,5 104,3 102,9 111,1 188,1 93,8 94,5 112,4 102,5 115,8 136,5 122,1 110,6 116,4 112,6 121,5 199,3

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 104.513888888889 3.45535199031559 30.2469586837500 Geometric Mean 101.530600039410 Harmonic Mean 99.3238126617825 Quadratic Mean 108.493568677800 Winsorized Mean ( 1 / 24 ) 104.443055555556 3.42641733943694 30.4817087963718 Winsorized Mean ( 2 / 24 ) 104.373611111111 3.39824876252711 30.7139407397278 Winsorized Mean ( 3 / 24 ) 104.052777777778 3.26096619382988 31.9085729789709 Winsorized Mean ( 4 / 24 ) 104.063888888889 3.23460619732639 32.1720427589931 Winsorized Mean ( 5 / 24 ) 103.751388888889 3.11940892204101 33.2599513182789 Winsorized Mean ( 6 / 24 ) 100.059722222222 1.85481509706403 53.9459282925861 Winsorized Mean ( 7 / 24 ) 98.6694444444444 1.50194532033017 65.6944318204302 Winsorized Mean ( 8 / 24 ) 98.625 1.48454709796355 66.4344028797002 Winsorized Mean ( 9 / 24 ) 98.4625 1.44127269101819 68.3163572123477 Winsorized Mean ( 10 / 24 ) 98.0597222222222 1.32746899872472 73.8696890973928 Winsorized Mean ( 11 / 24 ) 98.0291666666667 1.3068997071999 75.0089437824568 Winsorized Mean ( 12 / 24 ) 98.0458333333333 1.29953485343392 75.446867064977 Winsorized Mean ( 13 / 24 ) 97.4861111111111 1.18981775796368 81.9336494674231 Winsorized Mean ( 14 / 24 ) 97.4666666666667 1.18039541397505 82.5712007287811 Winsorized Mean ( 15 / 24 ) 97.2166666666667 1.13015641445189 86.0205414255115 Winsorized Mean ( 16 / 24 ) 97.1277777777778 1.10817177724411 87.6468610483141 Winsorized Mean ( 17 / 24 ) 96.7027777777778 0.995182001076643 97.1709472972375 Winsorized Mean ( 18 / 24 ) 96.3777777777778 0.935987637148297 102.969071334548 Winsorized Mean ( 19 / 24 ) 96.1138888888889 0.857858147227783 112.039372942352 Winsorized Mean ( 20 / 24 ) 95.8638888888889 0.81297023362795 117.918079806056 Winsorized Mean ( 21 / 24 ) 95.8347222222222 0.768606343301505 124.686353498684 Winsorized Mean ( 22 / 24 ) 95.6819444444444 0.721973274025593 132.528374507465 Winsorized Mean ( 23 / 24 ) 95.6819444444445 0.713384575374457 134.123932234196 Winsorized Mean ( 24 / 24 ) 95.7819444444444 0.674033030183333 142.102745941682 Trimmed Mean ( 1 / 24 ) 103.424285714286 3.23002954028521 32.0196098594051 Trimmed Mean ( 2 / 24 ) 102.345588235294 2.98566992600307 34.2789359747829 Trimmed Mean ( 3 / 24 ) 101.239393939394 2.69567803856269 37.5561890148328 Trimmed Mean ( 4 / 24 ) 100.184375 2.39791805650326 41.7797325176711 Trimmed Mean ( 5 / 24 ) 99.058064516129 2.00865334282709 49.3156596034184 Trimmed Mean ( 6 / 24 ) 97.9316666666667 1.50037940901564 65.2712681060567 Trimmed Mean ( 7 / 24 ) 97.4913793103448 1.38049300855135 70.6206976105222 Trimmed Mean ( 8 / 24 ) 97.275 1.34069726480073 72.555529539667 Trimmed Mean ( 9 / 24 ) 97.05 1.29515775597343 74.9329566629184 Trimmed Mean ( 10 / 24 ) 96.8326923076923 1.24882062357977 77.5393122753843 Trimmed Mean ( 11 / 24 ) 96.656 1.21827968371598 79.3381037966433 Trimmed Mean ( 12 / 24 ) 96.46875 1.18334765343198 81.5219007873285 Trimmed Mean ( 13 / 24 ) 96.2630434782609 1.13912992772051 84.505762806962 Trimmed Mean ( 14 / 24 ) 96.109090909091 1.10893840146481 86.667655103421 Trimmed Mean ( 15 / 24 ) 95.9428571428572 1.07052768939655 89.6220229454683 Trimmed Mean ( 16 / 24 ) 95.79 1.03186910320730 92.8315420068893 Trimmed Mean ( 17 / 24 ) 95.6315789473684 0.984756544442846 97.1118998772176 Trimmed Mean ( 18 / 24 ) 95.5055555555556 0.951364470779219 100.387977992631 Trimmed Mean ( 19 / 24 ) 95.4029411764706 0.92092417828024 103.594783834027 Trimmed Mean ( 20 / 24 ) 95.31875 0.898872922187522 106.042520190762 Trimmed Mean ( 21 / 24 ) 95.2533333333333 0.878514071133796 108.425506731384 Trimmed Mean ( 22 / 24 ) 95.1821428571429 0.859371826249894 110.757811636083 Trimmed Mean ( 23 / 24 ) 95.1192307692308 0.842761381152536 112.866147994523 Trimmed Mean ( 24 / 24 ) 95.0458333333333 0.815941244658155 116.486124406119 Median 94.15 Midrange 142.65 Midmean - Weighted Average at Xnp 95.291891891892 Midmean - Weighted Average at X(n+1)p 95.5055555555556 Midmean - Empirical Distribution Function 95.291891891892 Midmean - Empirical Distribution Function - Averaging 95.5055555555556 Midmean - Empirical Distribution Function - Interpolation 95.5055555555556 Midmean - Closest Observation 95.291891891892 Midmean - True Basic - Statistics Graphics Toolkit 95.5055555555556 Midmean - MS Excel (old versions) 95.6315789473684 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/20/t1287588585bmev3kuf0z6suxe/1d3h31287588647.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287588585bmev3kuf0z6suxe/1d3h31287588647.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287588585bmev3kuf0z6suxe/2d3h31287588647.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287588585bmev3kuf0z6suxe/2d3h31287588647.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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