WS3Part2Yt*Xt

*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: Mon, 19 Oct 2009 13:01:15 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/19/t1255979216v3qcz46st992urk.htm/, Retrieved Mon, 19 Oct 2009 21:06:58 +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/2009/Oct/19/t1255979216v3qcz46st992urk.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

ShwWs3V2

Dataseries X:

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6165561,6 4930198 5425516,8 4882416 5013277,2 4824106,6 4386552,8 3612685,5 3354824 4573662,5 3607962,5 2313181,2 6068078,55 5733506,24 5801696,32 5679979,04 4473715,68 4134416,13 3817990,84 2860636,2 3467462,88 4132339,8 3002307,36 2004734,61 5512120,68 4808915,54 5330777 4821427,17 4115383,8 4432005,74 3902015,55 3196453,24 3798522,75 4694299,6 3333356,94 2913313,14 5227244,4 5552024,24 6820771,05 5963048,74 4331811,21 4820109,95 3463539,62 3293941,28 3729726,82 4312980 3719352,72 2773137,94 5691542,88 5058654,3 5838951,24 5399831,16 4662499,05 5538644,5 3662097,01 3730770,83 3982615,85 4148178,34 3991276,66 2349702,88

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 4386464.20283333 138450.803920013 31.6824754977048 Geometric Mean 4247923.52141105 Harmonic Mean 4098252.02460502 Quadratic Mean 4513537.09234765 Winsorized Mean ( 1 / 20 ) 4380684.82183333 134164.218751368 32.651662735439 Winsorized Mean ( 2 / 20 ) 4378652.77616667 133132.132584694 32.8895263011063 Winsorized Mean ( 3 / 20 ) 4394573.03866667 126981.369963730 34.6080140726305 Winsorized Mean ( 4 / 20 ) 4392133.08933333 124055.350183799 35.4046244908099 Winsorized Mean ( 5 / 20 ) 4393418.25766667 122537.440470602 35.8536806448205 Winsorized Mean ( 6 / 20 ) 4395498.67166667 119434.572796549 36.8025653606529 Winsorized Mean ( 7 / 20 ) 4413253.299 114217.048530826 38.6391817663624 Winsorized Mean ( 8 / 20 ) 4424709.859 111633.898614466 39.635898359879 Winsorized Mean ( 9 / 20 ) 4411428.988 107057.858746764 41.2060267190181 Winsorized Mean ( 10 / 20 ) 4412776.87466667 106048.057982891 41.6111049895754 Winsorized Mean ( 11 / 20 ) 4427845.37133333 101886.605935391 43.4585619049980 Winsorized Mean ( 12 / 20 ) 4411309.24733333 98688.6355756975 44.6992627023373 Winsorized Mean ( 13 / 20 ) 4436185.60966667 92943.9020424368 47.7297112794035 Winsorized Mean ( 14 / 20 ) 4421175.00566667 89980.119885659 49.1350201720649 Winsorized Mean ( 15 / 20 ) 4407644.73316667 83740.4058768922 52.634623477302 Winsorized Mean ( 16 / 20 ) 4377955.5625 74201.5791838242 59.0008408265034 Winsorized Mean ( 17 / 20 ) 4368038.04583333 71779.6950455729 60.8533937495843 Winsorized Mean ( 18 / 20 ) 4343427.48883333 68009.101150478 63.8653858874417 Winsorized Mean ( 19 / 20 ) 4349751.29683333 62569.2837376954 69.5189562192925 Winsorized Mean ( 20 / 20 ) 4336804.1935 58832.0726230289 73.714965326624 Trimmed Mean ( 1 / 20 ) 4385557.69844828 130449.452855552 33.618827848243 Trimmed Mean ( 2 / 20 ) 4390778.63767857 125865.464706888 34.8846973067926 Trimmed Mean ( 3 / 20 ) 4397515.22740741 120869.11417177 36.3824559941591 Trimmed Mean ( 4 / 20 ) 4398646.83846154 117673.487407804 37.3801009501637 Trimmed Mean ( 5 / 20 ) 4400600.9632 114788.592227384 38.336570540763 Trimmed Mean ( 6 / 20 ) 4402396.63958333 111618.856555274 39.4413343358632 Trimmed Mean ( 7 / 20 ) 4403896.19782609 108513.845103317 40.5837263773402 Trimmed Mean ( 8 / 20 ) 4402073.38590909 106000.414624645 41.5288317644525 Trimmed Mean ( 9 / 20 ) 4398031.15857143 103361.033021909 42.550185790415 Trimmed Mean ( 10 / 20 ) 4395798.187 101057.110502282 43.4981582706219 Trimmed Mean ( 11 / 20 ) 4393117.34157895 98139.0270456466 44.7642235085091 Trimmed Mean ( 12 / 20 ) 4387855.51888889 95220.228264627 46.0811279163769 Trimmed Mean ( 13 / 20 ) 4384406.44117647 92016.5050706073 47.6480435527536 Trimmed Mean ( 14 / 20 ) 4376938.291875 89037.6327590336 49.1582958379015 Trimmed Mean ( 15 / 20 ) 4370618.76133333 85562.3033197377 51.0811255863551 Trimmed Mean ( 16 / 20 ) 4365329.33678571 82396.2856232546 52.9796859623693 Trimmed Mean ( 17 / 20 ) 4363508.24653846 80713.39876403 54.0617581883203 Trimmed Mean ( 18 / 20 ) 4362842.09958333 78604.6224425899 55.5036327891506 Trimmed Mean ( 19 / 20 ) 4365783.70727273 76291.7314186469 57.2248607560853 Trimmed Mean ( 20 / 20 ) 4368315.1405 74343.0134058674 58.758919505343 Median 4359182.005 Midrange 4412752.83 Midmean - Weighted Average at Xnp 4346169.30129032 Midmean - Weighted Average at X(n+1)p 4370618.76133333 Midmean - Empirical Distribution Function 4346169.30129032 Midmean - Empirical Distribution Function - Averaging 4370618.76133333 Midmean - Empirical Distribution Function - Interpolation 4370618.76133333 Midmean - Closest Observation 4346169.30129032 Midmean - True Basic - Statistics Graphics Toolkit 4370618.76133333 Midmean - MS Excel (old versions) 4376938.291875 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/19/t1255979216v3qcz46st992urk/1k9fa1255978873.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255979216v3qcz46st992urk/1k9fa1255978873.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255979216v3qcz46st992urk/2o1jq1255978873.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255979216v3qcz46st992urk/2o1jq1255978873.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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