textiel

*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: Sat, 20 Dec 2008 00:56:53 -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/20/t12297601028e5nowad10zuy5i.htm/, Retrieved Sat, 20 Dec 2008 09:01:44 +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/20/t12297601028e5nowad10zuy5i.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)

User-defined keywords:

Dataseries X:

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101.3 102 109.2 88.6 94.3 98.3 86.4 80.6 104.1 108.2 93.4 71.9 94.1 94.9 96.4 91.1 84.4 86.4 88 75.1 109.7 103 82.1 68 96.4 94.3 90 88 76.1 82.5 81.4 66.5 97.2 94.1 80.7 70.5 87.8 89.5 99.6 84.2 75.1 92 80.8 73.1 99.8 90 83.1 72.4 78.8 87.3 91 80.1 73.6 86.4 74.5 71.2 92.4 81.5 85.3 69.9 84.2 90.7 100.3 79.4 84.8 92.9 81.6 76 98.7 89.1 88.7 67.1

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 86.9736111111111 1.24480924284730 69.8690274119213 Geometric Mean 86.3349274151293 Harmonic Mean 85.690677783484 Quadratic Mean 87.603807470528 Winsorized Mean ( 1 / 24 ) 86.975 1.24113562705993 70.0769505795523 Winsorized Mean ( 2 / 24 ) 86.9722222222222 1.22871426340240 70.7831143600381 Winsorized Mean ( 3 / 24 ) 86.8805555555555 1.17351717591312 74.0343280344009 Winsorized Mean ( 4 / 24 ) 86.8527777777778 1.15445820917778 75.2325004814472 Winsorized Mean ( 5 / 24 ) 86.8319444444444 1.13147947380566 76.7419528631752 Winsorized Mean ( 6 / 24 ) 86.8319444444444 1.10940781759767 78.2687331629515 Winsorized Mean ( 7 / 24 ) 86.7833333333333 1.08277161312863 80.1492505724044 Winsorized Mean ( 8 / 24 ) 86.8055555555556 1.05871613144560 81.9913411889068 Winsorized Mean ( 9 / 24 ) 86.8430555555555 1.04311556770737 83.2535322489965 Winsorized Mean ( 10 / 24 ) 86.8430555555556 0.999854892423556 86.855658969729 Winsorized Mean ( 11 / 24 ) 86.8736111111111 0.973926504763362 89.1993499367995 Winsorized Mean ( 12 / 24 ) 86.6902777777778 0.94439943681306 91.7940803420213 Winsorized Mean ( 13 / 24 ) 86.7083333333333 0.894291035065801 96.9576233389765 Winsorized Mean ( 14 / 24 ) 86.7277777777778 0.891018087628589 97.3355973149776 Winsorized Mean ( 15 / 24 ) 86.9777777777778 0.75331614874616 115.459860939588 Winsorized Mean ( 16 / 24 ) 86.9777777777778 0.713631037385869 121.880598266003 Winsorized Mean ( 17 / 24 ) 87.1430555555555 0.689372223515235 126.409293242477 Winsorized Mean ( 18 / 24 ) 87.2180555555556 0.664301339097784 131.292909440782 Winsorized Mean ( 19 / 24 ) 87.2444444444444 0.660608888552183 132.066712931539 Winsorized Mean ( 20 / 24 ) 87.0777777777778 0.628727452086458 138.498450304351 Winsorized Mean ( 21 / 24 ) 87.1069444444445 0.583843929415936 149.195598439439 Winsorized Mean ( 22 / 24 ) 86.9847222222222 0.558515175076888 155.742808976045 Winsorized Mean ( 23 / 24 ) 86.8888888888889 0.536793920831022 161.866380219758 Winsorized Mean ( 24 / 24 ) 86.7555555555555 0.474184453031134 182.957401916042 Trimmed Mean ( 1 / 24 ) 86.9414285714286 1.20261704424228 72.2935276758918 Trimmed Mean ( 2 / 24 ) 86.9058823529412 1.15676026192494 75.1286893347484 Trimmed Mean ( 3 / 24 ) 86.869696969697 1.10996749085507 78.263280398218 Trimmed Mean ( 4 / 24 ) 86.865625 1.07972663985635 80.4514974378674 Trimmed Mean ( 5 / 24 ) 86.8693548387097 1.05034452988680 82.7055812325426 Trimmed Mean ( 6 / 24 ) 86.8783333333333 1.02206197824902 85.002999017899 Trimmed Mean ( 7 / 24 ) 86.8879310344828 0.99386830821424 87.4239879834794 Trimmed Mean ( 8 / 24 ) 86.9071428571429 0.9662783644225 89.9400690908394 Trimmed Mean ( 9 / 24 ) 86.924074074074 0.938146227999457 92.6551442406102 Trimmed Mean ( 10 / 24 ) 86.9365384615385 0.906795315348404 95.8722845057224 Trimmed Mean ( 11 / 24 ) 86.95 0.877758043924104 99.0591890349206 Trimmed Mean ( 12 / 24 ) 86.9604166666667 0.846973855923666 102.671901922914 Trimmed Mean ( 13 / 24 ) 86.995652173913 0.81436354640743 106.826554992171 Trimmed Mean ( 14 / 24 ) 87.0318181818182 0.784157165445271 110.987722891493 Trimmed Mean ( 15 / 24 ) 87.0690476190476 0.745123426666187 116.851845617859 Trimmed Mean ( 16 / 24 ) 87.08 0.727819011032628 119.645129736926 Trimmed Mean ( 17 / 24 ) 87.0921052631579 0.71323977421233 122.107751715527 Trimmed Mean ( 18 / 24 ) 87.0861111111111 0.69829898515116 124.711782435513 Trimmed Mean ( 19 / 24 ) 87.0705882352941 0.682823766509257 127.515462269888 Trimmed Mean ( 20 / 24 ) 87.05 0.660766905365127 131.740859436503 Trimmed Mean ( 21 / 24 ) 87.0466666666667 0.637645333144708 136.512669570362 Trimmed Mean ( 22 / 24 ) 87.0392857142857 0.61677046071401 141.121034904175 Trimmed Mean ( 23 / 24 ) 87.0461538461538 0.592471505818719 146.920405439359 Trimmed Mean ( 24 / 24 ) 87.0666666666667 0.561366947941848 155.097600572818 Median 87.55 Midrange 88.1 Midmean - Weighted Average at Xnp 86.8972972972973 Midmean - Weighted Average at X(n+1)p 87.0861111111111 Midmean - Empirical Distribution Function 86.8972972972973 Midmean - Empirical Distribution Function - Averaging 87.0861111111111 Midmean - Empirical Distribution Function - Interpolation 87.0861111111111 Midmean - Closest Observation 86.8972972972973 Midmean - True Basic - Statistics Graphics Toolkit 87.0861111111111 Midmean - MS Excel (old versions) 87.2769230769231 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297601028e5nowad10zuy5i/1qf4d1229759810.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297601028e5nowad10zuy5i/1qf4d1229759810.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297601028e5nowad10zuy5i/203wm1229759810.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297601028e5nowad10zuy5i/203wm1229759810.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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