Uitvoer Intra-EU

*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, 18 Oct 2008 04:25:00 -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/18/t12243256925gg1qhcv6qowqmi.htm/, Retrieved Sat, 18 Oct 2008 10:28:14 +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/18/t12243256925gg1qhcv6qowqmi.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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Dataseries X:

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12112 10875,2 9897,3 11672,1 12385,7 11405,6 9830,9 11025,1 10853,8 12252,6 11839,4 11669,1 11601,4 11178,4 9516,4 12102,8 12989 11610,2 10205,5 11356,2 11307,1 12648,6 11947,2 11714,1 12192,5 11268,8 9097,4 12639,8 13040,1 11687,3 11191,7 11391,9 11793,1 13933,2 12778,1 11810,3 13698,4 11956,6 10723,8 13938,9 13979,8 13807,4 12973,9 12509,8 12934,1 14908,3 13772,1 13012,6 14049,9 11816,5 11593,2 14466,2 13615,9 14733,9 13880,7 13527,5 13584 16170,2 13260,6 14741,9 15486,5 13154,5 12621,2 15031,6 15452,4 15428 13105,9 14716,8 14180 16202,2 14392,4 15140,6 15960,1 14351,3 13230,2 15202,1 17157,3 16159,1 13405,7 17224,7 17338,4 17370,6 18817,8 16593,2 17979,5

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 13249.1552941176 223.107961076100 59.3845025978184 Geometric Mean 13095.3917123946 Harmonic Mean 12945.358986721 Quadratic Mean 13406.0209473382 Winsorized Mean ( 1 / 28 ) 13244.2223529412 219.328494423412 60.3853247055685 Winsorized Mean ( 2 / 28 ) 13237.2952941176 214.391861949852 61.7434597270951 Winsorized Mean ( 3 / 28 ) 13238.5023529412 213.691899194721 61.9513533401561 Winsorized Mean ( 4 / 28 ) 13247.6552941176 209.875176211129 63.1215922400983 Winsorized Mean ( 5 / 28 ) 13274.1788235294 204.075376584229 65.045470187094 Winsorized Mean ( 6 / 28 ) 13243.5364705882 194.109504656240 68.2271406237525 Winsorized Mean ( 7 / 28 ) 13213.0988235294 187.481872061072 70.476674242005 Winsorized Mean ( 8 / 28 ) 13224.1952941176 184.863845475209 71.5347842090143 Winsorized Mean ( 9 / 28 ) 13239.2517647059 182.399003815125 72.5840135515479 Winsorized Mean ( 10 / 28 ) 13217.4047058824 177.806238779060 74.3360007873862 Winsorized Mean ( 11 / 28 ) 13166.0929411765 165.695075193514 79.459772270237 Winsorized Mean ( 12 / 28 ) 13166.6858823529 164.161650632063 80.2056133796044 Winsorized Mean ( 13 / 28 ) 13170.4635294118 162.538537665571 81.0297897259938 Winsorized Mean ( 14 / 28 ) 13139.1364705882 155.742556398440 84.3644587223423 Winsorized Mean ( 15 / 28 ) 13130.7011764706 153.719172787966 85.4200613906668 Winsorized Mean ( 16 / 28 ) 13145.4964705882 145.945754412193 90.0711125413183 Winsorized Mean ( 17 / 28 ) 13122.4764705882 141.993613978855 92.4159622596998 Winsorized Mean ( 18 / 28 ) 13089.1023529412 136.576517466157 95.8371365427781 Winsorized Mean ( 19 / 28 ) 13100.48 134.636690361865 97.3024512470537 Winsorized Mean ( 20 / 28 ) 13097.1623529412 133.967219672250 97.7639334830068 Winsorized Mean ( 21 / 28 ) 13039.0047058824 124.809386754945 104.471346626225 Winsorized Mean ( 22 / 28 ) 13026.84 121.335496112254 107.362152192860 Winsorized Mean ( 23 / 28 ) 13037.0952941176 117.119053531082 111.314896262014 Winsorized Mean ( 24 / 28 ) 12993.5847058824 110.166630190723 117.944832145520 Winsorized Mean ( 25 / 28 ) 12957.1435294118 105.109470684533 123.272845396589 Winsorized Mean ( 26 / 28 ) 12942.7058823529 101.573621894930 127.421919597799 Winsorized Mean ( 27 / 28 ) 12963.9564705882 95.6126244908933 135.588334067987 Winsorized Mean ( 28 / 28 ) 12965.1752941176 94.9930714251518 136.485483621122 Trimmed Mean ( 1 / 28 ) 13232.0843373494 212.432380297564 62.2884530070914 Trimmed Mean ( 2 / 28 ) 13219.3469135802 204.418955265581 64.6679115271168 Trimmed Mean ( 3 / 28 ) 13209.6911392405 198.198077070874 66.6489369345234 Trimmed Mean ( 4 / 28 ) 13199.0896103896 191.243637303945 69.0171437673099 Trimmed Mean ( 5 / 28 ) 13185.3293333333 184.464397861654 71.4789926196067 Trimmed Mean ( 6 / 28 ) 13164.6383561644 178.24164042286 73.8583774528366 Trimmed Mean ( 7 / 28 ) 13148.8957746479 173.652297364667 75.7196764695571 Trimmed Mean ( 8 / 28 ) 13137.5971014493 169.856378690360 77.3453266974357 Trimmed Mean ( 9 / 28 ) 13123.8641791045 165.894516527088 79.109692434961 Trimmed Mean ( 10 / 28 ) 13107.0984615385 161.63383232593 81.0913054088105 Trimmed Mean ( 11 / 28 ) 13092.2158730159 157.472792311932 83.1395422714166 Trimmed Mean ( 12 / 28 ) 13082.8573770492 154.881370899436 84.4701806361454 Trimmed Mean ( 13 / 28 ) 13072.7932203390 151.962548522665 86.0264147148678 Trimmed Mean ( 14 / 28 ) 13061.5894736842 148.638438666279 87.8749103588871 Trimmed Mean ( 15 / 28 ) 13053.0290909091 145.815260286694 89.5175790602777 Trimmed Mean ( 16 / 28 ) 13044.7245283019 142.638390008107 91.4531110983547 Trimmed Mean ( 17 / 28 ) 13034.2274509804 140.045595350535 93.0713130845398 Trimmed Mean ( 18 / 28 ) 13025.2224489796 137.462803480401 94.754523545249 Trimmed Mean ( 19 / 28 ) 13018.8042553191 135.153727732036 96.3258984697115 Trimmed Mean ( 20 / 28 ) 13010.6844444444 132.432594288015 98.2438236930458 Trimmed Mean ( 21 / 28 ) 13002.1372093023 128.928277297332 100.847831692632 Trimmed Mean ( 22 / 28 ) 12998.4975609756 126.267757432072 102.943917159283 Trimmed Mean ( 23 / 28 ) 12995.6897435897 123.365064477485 105.343354689865 Trimmed Mean ( 24 / 28 ) 12991.5540540541 120.278498436358 108.012273373434 Trimmed Mean ( 25 / 28 ) 12991.3485714286 117.616980236086 110.454702589301 Trimmed Mean ( 26 / 28 ) 12994.8727272727 114.980882656107 113.017681088244 Trimmed Mean ( 27 / 28 ) 13000.3741935484 111.946703713975 116.130031186666 Trimmed Mean ( 28 / 28 ) 13004.3275862069 109.095927293973 119.200852944447 Median 13012.6 Midrange 13957.6 Midmean - Weighted Average at Xnp 12967.2785714286 Midmean - Weighted Average at X(n+1)p 13002.1372093023 Midmean - Empirical Distribution Function 13002.1372093023 Midmean - Empirical Distribution Function - Averaging 13002.1372093023 Midmean - Empirical Distribution Function - Interpolation 13002.1372093023 Midmean - Closest Observation 12971.9090909091 Midmean - True Basic - Statistics Graphics Toolkit 13002.1372093023 Midmean - MS Excel (old versions) 13002.1372093023 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/18/t12243256925gg1qhcv6qowqmi/1gyi41224325498.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/18/t12243256925gg1qhcv6qowqmi/1gyi41224325498.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/18/t12243256925gg1qhcv6qowqmi/2zxoh1224325498.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/18/t12243256925gg1qhcv6qowqmi/2zxoh1224325498.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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