Central Tendency Bouwvergunningen in Belgie

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 17 Oct 2008 09:13:04 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/17/t1224256558rtnlpdmrd2e0gn5.htm/, Retrieved Fri, 17 Oct 2008 15:15:58 +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/Oct/17/t1224256558rtnlpdmrd2e0gn5.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}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

CT Belgie

Dataseries X:

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3353 3480 3098 2944 3389 3497 4404 3849 3734 3060 3507 3287 3215 3764 2734 2837 2766 3851 3289 3848 3348 3682 4058 3655 3811 3341 3032 3475 3353 3186 3902 4164 3499 4145 3796 3711 3949 3740 3243 4407 4814 3908 5250 3937 4004 5560 3922 3759 4138 4634 3996 4308 4142 4429 5219 4929 5754 5592 4163 4962 5208 4755 4491 5732 5730 5024 6056 4901 5353 5578 4618 4724 5011 5298 4143 4617 4727 4207 5112 4190 4098 5071 4177 4598 3757 5591 4218 3780 4336 4870 4422 4727 4459

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4197.87096774194 81.453535264925 51.5370014829742 Geometric Mean 4125.76423019294 Harmonic Mean 4054.47885617757 Quadratic Mean 4269.95445821953 Winsorized Mean ( 1 / 31 ) 4194.96774193548 80.642692856098 52.0191922338351 Winsorized Mean ( 2 / 31 ) 4196.02150537634 80.256193302841 52.2828374072386 Winsorized Mean ( 3 / 31 ) 4199.40860215054 79.629260511639 52.7370036487622 Winsorized Mean ( 4 / 31 ) 4197.25806451613 77.797814733954 53.950847833831 Winsorized Mean ( 5 / 31 ) 4198.70967741936 77.5446448504656 54.1457077470146 Winsorized Mean ( 6 / 31 ) 4200.32258064516 76.9948104255487 54.5533206384959 Winsorized Mean ( 7 / 31 ) 4205.59139784946 75.7310826295322 55.5332269369862 Winsorized Mean ( 8 / 31 ) 4190.27956989247 72.0688472159429 58.1427306216924 Winsorized Mean ( 9 / 31 ) 4187.66666666667 70.7521375511271 59.1878466377156 Winsorized Mean ( 10 / 31 ) 4187.23655913978 69.203152361959 60.5064424990199 Winsorized Mean ( 11 / 31 ) 4183.8064516129 68.5627193443058 61.0215944120129 Winsorized Mean ( 12 / 31 ) 4189.09677419355 67.3946896617534 62.1576684337916 Winsorized Mean ( 13 / 31 ) 4176.65591397849 65.1088248120174 64.1488450457731 Winsorized Mean ( 14 / 31 ) 4171.23655913978 64.0513275176015 65.123342806494 Winsorized Mean ( 15 / 31 ) 4163.65591397849 62.909003003265 66.1853743535309 Winsorized Mean ( 16 / 31 ) 4167.61290322581 61.7181722012567 67.5265121208653 Winsorized Mean ( 17 / 31 ) 4174.37634408602 58.2905618536182 71.6132459757189 Winsorized Mean ( 18 / 31 ) 4168.95698924731 57.2340729839045 72.8404737230516 Winsorized Mean ( 19 / 31 ) 4166.70967741936 55.9600943533748 74.4585892065794 Winsorized Mean ( 20 / 31 ) 4160.47311827957 54.960752691945 75.698983629264 Winsorized Mean ( 21 / 31 ) 4149.63440860215 52.9739538021031 78.3334848688867 Winsorized Mean ( 22 / 31 ) 4170.68817204301 46.6476777431128 89.4082701182008 Winsorized Mean ( 23 / 31 ) 4170.44086021505 44.9138452764197 92.8542375863905 Winsorized Mean ( 24 / 31 ) 4177.92473118280 44.0401853249888 94.8661932358446 Winsorized Mean ( 25 / 31 ) 4183.30107526882 43.2251187323036 96.7794004494542 Winsorized Mean ( 26 / 31 ) 4159.81720430108 39.686296012848 104.817471576445 Winsorized Mean ( 27 / 31 ) 4160.10752688172 38.5200428766345 107.998517556302 Winsorized Mean ( 28 / 31 ) 4160.40860215054 38.4126977985713 108.308159556168 Winsorized Mean ( 29 / 31 ) 4156.04301075269 37.4729602185437 110.907784880471 Winsorized Mean ( 30 / 31 ) 4126.68817204301 32.5620491522939 126.733061323700 Winsorized Mean ( 31 / 31 ) 4121.35483870968 30.6584688509785 134.427940897582 Trimmed Mean ( 1 / 31 ) 4193.53846153846 79.0426838023882 53.054100136865 Trimmed Mean ( 2 / 31 ) 4192.04494382022 77.2152697532853 54.2903619609755 Trimmed Mean ( 3 / 31 ) 4189.91954022988 75.3570600929441 55.6008890880577 Trimmed Mean ( 4 / 31 ) 4186.45882352941 73.4911255393244 56.9655015188096 Trimmed Mean ( 5 / 31 ) 4183.43373493976 71.9707780040164 58.1268377383151 Trimmed Mean ( 6 / 31 ) 4179.92592592593 70.2830779243767 59.4727215905862 Trimmed Mean ( 7 / 31 ) 4175.92405063291 68.4635567896774 60.9948452351301 Trimmed Mean ( 8 / 31 ) 4170.80519480520 66.6363690981851 62.5905230319458 Trimmed Mean ( 9 / 31 ) 4167.78666666667 65.3106541626031 63.8148051050014 Trimmed Mean ( 10 / 31 ) 4164.97260273973 64.0173230117211 65.0600869701651 Trimmed Mean ( 11 / 31 ) 4162.05633802817 62.7849765037548 66.2906410067584 Trimmed Mean ( 12 / 31 ) 4159.39130434783 61.4399193544199 67.6985150379857 Trimmed Mean ( 13 / 31 ) 4159.39130434783 60.0420568448184 69.2746305326943 Trimmed Mean ( 14 / 31 ) 4153.67692307692 58.7824669196501 70.6618340593734 Trimmed Mean ( 15 / 31 ) 4151.8253968254 57.4496219108286 72.2689768658482 Trimmed Mean ( 16 / 31 ) 4150.62295081967 56.0364204553655 74.0700943616795 Trimmed Mean ( 17 / 31 ) 4148.94915254237 54.5214847475902 76.0975085647452 Trimmed Mean ( 18 / 31 ) 4146.50877192982 53.2661669176564 77.8450752489825 Trimmed Mean ( 19 / 31 ) 4144.4 51.8994145014106 79.8544654080319 Trimmed Mean ( 20 / 31 ) 4142.33962264151 50.4265041884791 82.1460795132395 Trimmed Mean ( 21 / 31 ) 4140.68627450980 48.7672784076684 84.9070608348466 Trimmed Mean ( 22 / 31 ) 4139.87755102041 47.0633766566322 87.9638871053468 Trimmed Mean ( 23 / 31 ) 4137.10638297872 46.1052292956232 89.7318253522158 Trimmed Mean ( 24 / 31 ) 4134.11111111111 45.1722094577537 91.5189042275527 Trimmed Mean ( 25 / 31 ) 4130.16279069767 44.0793346265722 93.6983923574904 Trimmed Mean ( 26 / 31 ) 4130.16279069767 42.7592182295818 96.5911670443109 Trimmed Mean ( 27 / 31 ) 4122.17948717949 41.8118959722876 98.5886765314737 Trimmed Mean ( 28 / 31 ) 4118.64864864865 40.7440965752102 101.085776709909 Trimmed Mean ( 29 / 31 ) 4114.68571428571 39.246875836239 104.841102039678 Trimmed Mean ( 30 / 31 ) 4110.66666666667 37.3845613762276 109.956263102784 Trimmed Mean ( 31 / 31 ) 4109.06451612903 36.2458432317172 113.366503570080 Median 4142 Midrange 4395 Midmean - Weighted Average at Xnp 4137.10638297872 Midmean - Weighted Average at X(n+1)p 4137.10638297872 Midmean - Empirical Distribution Function 4137.10638297872 Midmean - Empirical Distribution Function - Averaging 4137.10638297872 Midmean - Empirical Distribution Function - Interpolation 4137.10638297872 Midmean - Closest Observation 4127.0625 Midmean - True Basic - Statistics Graphics Toolkit 4137.10638297872 Midmean - MS Excel (old versions) 4137.10638297872 Number of observations 93

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/17/t1224256558rtnlpdmrd2e0gn5/1pcfc1224256378.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/17/t1224256558rtnlpdmrd2e0gn5/1pcfc1224256378.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/17/t1224256558rtnlpdmrd2e0gn5/2d4rs1224256378.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/17/t1224256558rtnlpdmrd2e0gn5/2d4rs1224256378.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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