gehuwde mannen

*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: Thu, 25 Nov 2010 20:20:42 +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/Nov/25/t1290716373mrnrz94w9ha4nld.htm/, Retrieved Thu, 25 Nov 2010 21:19:35 +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/2010/Nov/25/t1290716373mrnrz94w9ha4nld.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 54 222 522 1084 2023 3229 5198 8080 11132 14877 18448 21418 24525 26708 30336 33613 36727 39660 42131 43769 45025 46760 49.385 51.382 53.800 54.017 53.313 53.577 53.629 54.090 53.725 52.995 52.453 52.220 51.870 51.122 51.296 49.265 50.020 50.058 50.799 50.216 50.571 42.873 42.535 40.069 35.293 31.552 34.590 36.992 37.279 35.618 33.745 32.570 32.227 31.114 30.698 29.453 27.620 24.178 22.031 19.962 17.784 16.259 14.147 11.990 9.988 8.383 6.661 4.111 2.154 1.601 1.295 1.137 876 515 342 206 126 52 33 17

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4595.14712 1160.52781960247 3.95953207013514 Geometric Mean 0 Harmonic Mean 0 Quadratic Mean 12427.8330468952 Winsorized Mean ( 1 / 33 ) 4577.79712 1154.27329895611 3.96595600378178 Winsorized Mean ( 2 / 33 ) 4552.67712 1145.48384313094 3.97445773443318 Winsorized Mean ( 3 / 33 ) 4503.53712 1128.71199778431 3.98997895728987 Winsorized Mean ( 4 / 33 ) 4404.69712 1096.0044701144 4.01886784233667 Winsorized Mean ( 5 / 33 ) 4258.04712 1049.24018658506 4.05821962829939 Winsorized Mean ( 6 / 33 ) 4071.20712 991.904118286822 4.10443614956618 Winsorized Mean ( 7 / 33 ) 3841.81712 924.139849751506 4.15718153592558 Winsorized Mean ( 8 / 33 ) 3551.57712 841.708339275539 4.21948667285019 Winsorized Mean ( 9 / 33 ) 3355.10712 787.721613228767 4.25925487336555 Winsorized Mean ( 10 / 33 ) 3044.40712 704.558516608227 4.32101386646477 Winsorized Mean ( 11 / 33 ) 2717.70712 619.564266494756 4.38648138211018 Winsorized Mean ( 12 / 33 ) 2289.18712 511.160824591668 4.47840877052477 Winsorized Mean ( 13 / 33 ) 1802.33712 391.793730483482 4.60021940059091 Winsorized Mean ( 14 / 33 ) 1375.05712 290.340518441471 4.73601523955808 Winsorized Mean ( 15 / 33 ) 942.75712 190.887765009168 4.93880328031878 Winsorized Mean ( 16 / 33 ) 627.71712 120.90967781565 5.19162015266532 Winsorized Mean ( 17 / 33 ) 422.86712 76.9194239515602 5.49753363033893 Winsorized Mean ( 18 / 33 ) 253.87178 42.0394011334307 6.03890096327075 Winsorized Mean ( 19 / 33 ) 214.3818 34.2297659815270 6.26302266032719 Winsorized Mean ( 20 / 33 ) 143.643 20.6813322825883 6.94553900286848 Winsorized Mean ( 21 / 33 ) 142.28913 20.4018205749055 6.97433493631531 Winsorized Mean ( 22 / 33 ) 104.65967 13.4408623607422 7.7866782049408 Winsorized Mean ( 23 / 33 ) 77.64617 8.55738673522313 9.07358430820942 Winsorized Mean ( 24 / 33 ) 74.21945 7.87064373502651 9.4299084672964 Winsorized Mean ( 25 / 33 ) 54.6207 4.5229309138896 12.0763949394548 Winsorized Mean ( 26 / 33 ) 36.44462 1.81133729613222 20.1202835484152 Winsorized Mean ( 27 / 33 ) 37.0073 1.73080978697454 21.3814945342369 Winsorized Mean ( 28 / 33 ) 37.5939 1.65230239323402 22.7524333039415 Winsorized Mean ( 29 / 33 ) 37.75079 1.61856032414238 23.3236842871475 Winsorized Mean ( 30 / 33 ) 37.96349 1.58595945440263 23.9372386819935 Winsorized Mean ( 31 / 33 ) 38.60891 1.49706987395176 25.7896512860054 Winsorized Mean ( 32 / 33 ) 39.25435 1.41293933047067 27.7820492030070 Winsorized Mean ( 33 / 33 ) 39.87574 1.3177114871464 30.2613587184808 Trimmed Mean ( 1 / 33 ) 4211.7827755102 1100.85618983033 3.82591551414118 Trimmed Mean ( 2 / 33 ) 3830.51783333333 1037.81357444132 3.69094982728028 Trimmed Mean ( 3 / 33 ) 3446.39055319149 968.45313552895 3.55865495887846 Trimmed Mean ( 4 / 33 ) 3063.36643478261 893.06807808969 3.43016004035804 Trimmed Mean ( 5 / 33 ) 2690.77457777778 814.664975800227 3.30292163982463 Trimmed Mean ( 6 / 33 ) 2334.57627272727 735.2875015538 3.17505229967037 Trimmed Mean ( 7 / 33 ) 1998.01990697674 655.990765379506 3.04580492961794 Trimmed Mean ( 8 / 33 ) 1684.44895238095 578.14158964467 2.91355782485087 Trimmed Mean ( 9 / 33 ) 1399.82575609756 505.125285656575 2.77124467106815 Trimmed Mean ( 10 / 33 ) 1128.2589 426.956320675941 2.64256282285219 Trimmed Mean ( 11 / 33 ) 882.598871794872 349.689403645905 2.52395086208729 Trimmed Mean ( 12 / 33 ) 663.088315789474 271.915047829290 2.43858631981914 Trimmed Mean ( 13 / 33 ) 479.969081081081 200.189207779484 2.39757720411074 Trimmed Mean ( 14 / 33 ) 338.690444444444 140.808506517031 2.40532658730728 Trimmed Mean ( 15 / 33 ) 232.938742857143 91.6044936100376 2.5428746306788 Trimmed Mean ( 16 / 33 ) 163.348705882353 58.3181360958422 2.80099325557832 Trimmed Mean ( 17 / 33 ) 119.374424242424 37.2180979650764 3.2074294703195 Trimmed Mean ( 18 / 33 ) 91.479875 23.6482250630295 3.86836114575953 Trimmed Mean ( 19 / 33 ) 76.928629032258 18.1688419971766 4.23409642971262 Trimmed Mean ( 20 / 33 ) 64.8713333333333 12.9700413916651 5.00162885949009 Trimmed Mean ( 21 / 33 ) 58.0806724137931 10.7191710412178 5.41839216768339 Trimmed Mean ( 22 / 33 ) 50.9200892857143 7.3211814587625 6.955173775234 Trimmed Mean ( 23 / 33 ) 46.3965555555556 5.18907015105898 8.94120800160835 Trimmed Mean ( 24 / 33 ) 43.7837115384615 4.08677609604786 10.7135087681468 Trimmed Mean ( 25 / 33 ) 41.2474 2.58757100062304 15.9405867472114 Trimmed Mean ( 26 / 33 ) 40.1329583333333 1.90467238554027 21.0707934015379 Trimmed Mean ( 27 / 33 ) 40.4413478260870 1.86411118741630 21.6947079654296 Trimmed Mean ( 28 / 33 ) 40.7304090909091 1.82675922805715 22.2965393935510 Trimmed Mean ( 29 / 33 ) 40.7304090909091 1.79296886050200 22.7167409251633 Trimmed Mean ( 30 / 33 ) 41.276975 1.75281265417186 23.5489941847219 Trimmed Mean ( 31 / 33 ) 41.5676315789474 1.70406299362199 24.3932482158980 Trimmed Mean ( 32 / 33 ) 41.83275 1.65902430226801 25.2152725808847 Trimmed Mean ( 33 / 33 ) 42.0697352941176 1.61764706677200 26.0067453267587 Median 42.704 Midrange 23380 Midmean - Weighted Average at Xnp 40.603 Midmean - Weighted Average at X(n+1)p 41.2474 Midmean - Empirical Distribution Function 40.603 Midmean - Empirical Distribution Function - Averaging 41.2474 Midmean - Empirical Distribution Function - Interpolation 41.2474 Midmean - Closest Observation 40.603 Midmean - True Basic - Statistics Graphics Toolkit 41.2474 Midmean - MS Excel (old versions) 43.7837115384615 Number of observations 100

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716373mrnrz94w9ha4nld/18fzx1290716440.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716373mrnrz94w9ha4nld/18fzx1290716440.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716373mrnrz94w9ha4nld/2j6hi1290716440.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716373mrnrz94w9ha4nld/2j6hi1290716440.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')

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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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