ws seatbelt Q3

*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, 01 Dec 2008 04:21:23 -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/01/t12281305908rpki9u85odo0ce.htm/, Retrieved Mon, 01 Dec 2008 11:23:10 +0000

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/01/t12281305908rpki9u85odo0ce.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

98,5 96,7 113,1 100 104,7 108,5 90,5 88,6 105,4 119,9 107,2 84,1 101,4 105,1 118,7 113,8 113,8 118,9 98,5 91 120,7 127,9 112,4 93,1 107,5 107,3 114,8 120,8 112,2 123,3 100,6 86,7 123,6 125,3 111,1 98,4 102,3 105 128,2 124,7 116,1 131,2 97,7 88,8 132,8 113,9 112,6 104,3 107,5 106 117,3 123,1 114,3 132 92,3 93,7 121,3 113,6 116,3 98,3 111,9 109,3 133,2 118 131,6 134,1 96,7 99,8 128,3 134,9 130,7 107,3 121,6 120,6 140,5 124,8 129,9 159,4 111 110,1 132,7 135 118,6 94 117,9 114,7 113,6 130,6 117,1 123,2 106,1 87,9

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 113.070652173913 1.48484744989472 76.1496759696964 Geometric Mean 112.182003592449 Harmonic Mean 111.290470715128 Quadratic Mean 113.954405928138 Winsorized Mean ( 1 / 30 ) 112.893478260870 1.4215231801875 79.4172615925819 Winsorized Mean ( 2 / 30 ) 112.8 1.39306863769733 80.972320349163 Winsorized Mean ( 3 / 30 ) 112.819565217391 1.38806791438707 81.2781305929178 Winsorized Mean ( 4 / 30 ) 112.793478260870 1.38041363960469 81.7099129020274 Winsorized Mean ( 5 / 30 ) 112.836956521739 1.35502966488447 83.2726835772702 Winsorized Mean ( 6 / 30 ) 112.843478260870 1.34488493580625 83.9056749440206 Winsorized Mean ( 7 / 30 ) 112.934782608696 1.32635675903127 85.1466106986028 Winsorized Mean ( 8 / 30 ) 112.943478260870 1.3047263346328 86.5648797474883 Winsorized Mean ( 9 / 30 ) 112.963043478261 1.28875073064998 87.6531363216287 Winsorized Mean ( 10 / 30 ) 112.952173913043 1.27654282422691 88.4828708989445 Winsorized Mean ( 11 / 30 ) 113.215217391304 1.21666142119086 93.054004523699 Winsorized Mean ( 12 / 30 ) 113.202173913043 1.21460492246658 93.2008193109872 Winsorized Mean ( 13 / 30 ) 113.244565217391 1.17834149821183 96.1050471270366 Winsorized Mean ( 14 / 30 ) 113.092391304348 1.12818348607418 100.242906140989 Winsorized Mean ( 15 / 30 ) 113.092391304348 1.12342498304791 100.667506073723 Winsorized Mean ( 16 / 30 ) 113.057608695652 1.11324844769546 101.556493458125 Winsorized Mean ( 17 / 30 ) 112.577173913043 1.04584485248659 107.642327296808 Winsorized Mean ( 18 / 30 ) 112.733695652174 0.9958145534576 113.207519673967 Winsorized Mean ( 19 / 30 ) 112.754347826087 0.987186677955115 114.217858024228 Winsorized Mean ( 20 / 30 ) 112.645652173913 0.937450636436949 120.161689368579 Winsorized Mean ( 21 / 30 ) 112.759782608696 0.903145297309408 124.852316614638 Winsorized Mean ( 22 / 30 ) 112.951086956522 0.870719335337058 129.721578897519 Winsorized Mean ( 23 / 30 ) 113.426086956522 0.802504246922567 141.340170337399 Winsorized Mean ( 24 / 30 ) 113.139130434783 0.738844341922163 153.129859721795 Winsorized Mean ( 25 / 30 ) 113.139130434783 0.718435080196599 157.479963817778 Winsorized Mean ( 26 / 30 ) 113.026086956522 0.697435527668146 162.059548836609 Winsorized Mean ( 27 / 30 ) 113.084782608696 0.6828979289912 165.595439388355 Winsorized Mean ( 28 / 30 ) 113.236956521739 0.656808069682214 172.404941030227 Winsorized Mean ( 29 / 30 ) 113.047826086957 0.626111011110874 180.555562960604 Winsorized Mean ( 30 / 30 ) 113.080434782609 0.5440975449227 207.831179974675 Trimmed Mean ( 1 / 30 ) 112.877777777778 1.38969344986177 81.2249476954831 Trimmed Mean ( 2 / 30 ) 112.861363636364 1.35328312401216 83.3981903962246 Trimmed Mean ( 3 / 30 ) 112.894186046512 1.32882013087628 84.9582147525597 Trimmed Mean ( 4 / 30 ) 112.921428571429 1.30278406970144 86.6770105634672 Trimmed Mean ( 5 / 30 ) 112.957317073171 1.27531402688591 88.5721592422163 Trimmed Mean ( 6 / 30 ) 112.985 1.25085805992365 90.3259959062795 Trimmed Mean ( 7 / 30 ) 113.012820512821 1.22498460234074 92.2565233039439 Trimmed Mean ( 8 / 30 ) 113.026315789474 1.19911570988287 94.2580560474134 Trimmed Mean ( 9 / 30 ) 113.039189189189 1.17347870365371 96.328283450934 Trimmed Mean ( 10 / 30 ) 113.05 1.14656730653695 98.5986599787602 Trimmed Mean ( 11 / 30 ) 113.062857142857 1.11715249422646 101.206288064678 Trimmed Mean ( 12 / 30 ) 113.044117647059 1.09363507393786 103.365483003412 Trimmed Mean ( 13 / 30 ) 113.044117647059 1.06587086559590 106.057986286977 Trimmed Mean ( 14 / 30 ) 113.0015625 1.03917915415107 108.741175232979 Trimmed Mean ( 15 / 30 ) 112.991935483871 1.01599398513331 111.213193323232 Trimmed Mean ( 16 / 30 ) 112.981666666667 0.98859739615077 114.284811093551 Trimmed Mean ( 17 / 30 ) 112.974137931034 0.956945383340069 118.057038466204 Trimmed Mean ( 18 / 30 ) 113.0125 0.930357641398775 121.472103813849 Trimmed Mean ( 19 / 30 ) 113.038888888889 0.906608306277274 124.683270720352 Trimmed Mean ( 20 / 30 ) 113.065384615385 0.878423638744692 128.713959447813 Trimmed Mean ( 21 / 30 ) 113.104 0.852348304775144 132.696926088024 Trimmed Mean ( 22 / 30 ) 113.135416666667 0.8259235620496 136.980492947690 Trimmed Mean ( 23 / 30 ) 113.152173913043 0.798614374485355 141.685621406403 Trimmed Mean ( 24 / 30 ) 113.127272727273 0.777208125104854 145.555957372436 Trimmed Mean ( 25 / 30 ) 113.126190476190 0.762073242841024 148.445299108592 Trimmed Mean ( 26 / 30 ) 113.126190476190 0.745591745717488 151.726720589333 Trimmed Mean ( 27 / 30 ) 113.134210526316 0.727388167662248 155.534851343427 Trimmed Mean ( 28 / 30 ) 113.138888888889 0.705334298516058 160.404632423122 Trimmed Mean ( 29 / 30 ) 113.129411764706 0.680915413664734 166.143120708394 Trimmed Mean ( 30 / 30 ) 113.1375 0.654509019381408 172.858580477514 Median 113.6 Midrange 121.75 Midmean - Weighted Average at Xnp 112.921276595745 Midmean - Weighted Average at X(n+1)p 113.152173913043 Midmean - Empirical Distribution Function 112.921276595745 Midmean - Empirical Distribution Function - Averaging 113.152173913043 Midmean - Empirical Distribution Function - Interpolation 113.152173913043 Midmean - Closest Observation 112.921276595745 Midmean - True Basic - Statistics Graphics Toolkit 113.152173913043 Midmean - MS Excel (old versions) 113.135416666667 Number of observations 92

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/01/t12281305908rpki9u85odo0ce/1bwgb1228130477.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/01/t12281305908rpki9u85odo0ce/1bwgb1228130477.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/01/t12281305908rpki9u85odo0ce/2jv5r1228130477.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/01/t12281305908rpki9u85odo0ce/2jv5r1228130477.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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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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