Paper: Central Tendency Uitvoer 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: Tue, 16 Dec 2008 08:47:28 -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/16/t1229442507kjism7no67cdovj.htm/, Retrieved Tue, 16 Dec 2008 16:48:27 +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/16/t1229442507kjism7no67cdovj.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?

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Dataseries X:

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11178,4 9516,4 12102,8 12989,0 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 13584,0 16170,2 13260,6 14741,9 15486,5 13154,5 12621,2 15031,6 15452,4 15428 13105,9 14716,8 14180,0 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 17015,2

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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 13640.7287671233 240.117875974603 56.8084683897755 Geometric Mean 13489.5812286118 Harmonic Mean 13339.0313653266 Quadratic Mean 13792.0540925683 Winsorized Mean ( 1 / 24 ) 13634.9849315068 235.472812165049 57.9047101282748 Winsorized Mean ( 2 / 24 ) 13637.1821917808 227.147575859746 60.0366618052802 Winsorized Mean ( 3 / 24 ) 13657.1589041096 222.658383881264 61.3368275923194 Winsorized Mean ( 4 / 24 ) 13675.8383561644 216.961433058195 63.033499380031 Winsorized Mean ( 5 / 24 ) 13672.1328767123 215.773678080565 63.3633026898092 Winsorized Mean ( 6 / 24 ) 13666.7904109589 212.180126499385 64.4112652605025 Winsorized Mean ( 7 / 24 ) 13629.9972602740 203.057433878872 67.1238525963276 Winsorized Mean ( 8 / 24 ) 13592.5287671233 193.842753017910 70.1214182913889 Winsorized Mean ( 9 / 24 ) 13592.9849315068 192.404626353631 70.6479110669802 Winsorized Mean ( 10 / 24 ) 13619.0397260274 187.863238521799 72.4944370872594 Winsorized Mean ( 11 / 24 ) 13591.6150684932 181.94980476034 74.6998057315626 Winsorized Mean ( 12 / 24 ) 13526.4369863014 166.591847401516 81.1950716513769 Winsorized Mean ( 13 / 24 ) 13525.1369863014 164.872750751253 82.03379227115 Winsorized Mean ( 14 / 24 ) 13535.6082191781 161.824029445293 83.6439944399852 Winsorized Mean ( 15 / 24 ) 13492.7246575342 153.937870564195 87.6504566945244 Winsorized Mean ( 16 / 24 ) 13480.6041095890 151.667106495403 88.8828462617085 Winsorized Mean ( 17 / 24 ) 13485.6575342466 143.243923038678 94.14470958468 Winsorized Mean ( 18 / 24 ) 13457.5726027397 138.403765054841 97.2341510898008 Winsorized Mean ( 19 / 24 ) 13452.3150684932 126.494106318437 106.347366371586 Winsorized Mean ( 20 / 24 ) 13474.698630137 122.576109964349 109.929240159898 Winsorized Mean ( 21 / 24 ) 13561.0575342466 109.094763502121 124.305302096218 Winsorized Mean ( 22 / 24 ) 13519.1068493151 93.739330784651 144.220219369528 Winsorized Mean ( 23 / 24 ) 13501.7150684931 89.723597055691 150.481205742484 Winsorized Mean ( 24 / 24 ) 13491.0958904110 87.4828246991678 154.214223612504 Trimmed Mean ( 1 / 24 ) 13631.8028169014 226.775800423754 60.1113645787116 Trimmed Mean ( 2 / 24 ) 13628.4362318841 216.415869274586 62.9733682542127 Trimmed Mean ( 3 / 24 ) 13623.6716417910 209.472590548002 65.0379680040721 Trimmed Mean ( 4 / 24 ) 13611.1353846154 203.227105419211 66.9749999958851 Trimmed Mean ( 5 / 24 ) 13592.3920634921 197.795740443368 68.7193365894742 Trimmed Mean ( 6 / 24 ) 13573.3065573770 191.571679402280 70.8523650245532 Trimmed Mean ( 7 / 24 ) 13554.0288135593 185.018697904376 73.2576164846028 Trimmed Mean ( 8 / 24 ) 13540.1298245614 179.498538645082 75.4330922511518 Trimmed Mean ( 9 / 24 ) 13531.4363636364 175.027693438673 77.3102592954957 Trimmed Mean ( 10 / 24 ) 13522.0169811321 169.777075529771 79.6457174146632 Trimmed Mean ( 11 / 24 ) 13508.1294117647 164.203687386509 82.264470589925 Trimmed Mean ( 12 / 24 ) 13496.8224489796 158.563263390843 85.1194795083853 Trimmed Mean ( 13 / 24 ) 13492.9893617021 154.938486771416 87.0861052206393 Trimmed Mean ( 14 / 24 ) 13488.9777777778 150.581984109227 89.5789616372255 Trimmed Mean ( 15 / 24 ) 13483.3232558140 145.54892035069 92.6377414777576 Trimmed Mean ( 16 / 24 ) 13482.2073170732 140.785978263074 95.7638500893901 Trimmed Mean ( 17 / 24 ) 13482.3948717949 134.929095737357 99.9220723900698 Trimmed Mean ( 18 / 24 ) 13482.0162162162 129.169850847908 104.374326731171 Trimmed Mean ( 19 / 24 ) 13484.8485714286 122.518253990433 110.063995626982 Trimmed Mean ( 20 / 24 ) 13488.6363636364 116.661457552932 115.622045588760 Trimmed Mean ( 21 / 24 ) 13490.2774193548 109.452770558830 123.252041501352 Trimmed Mean ( 22 / 24 ) 13481.7931034483 103.352273257359 130.445056296701 Trimmed Mean ( 23 / 24 ) 13477.2074074074 99.5952565441485 135.3197719957 Trimmed Mean ( 24 / 24 ) 13474.096 95.0808283304263 141.712017412960 Median 13527.5 Midrange 13957.6 Midmean - Weighted Average at Xnp 13442.3972222222 Midmean - Weighted Average at X(n+1)p 13482.0162162162 Midmean - Empirical Distribution Function 13482.0162162162 Midmean - Empirical Distribution Function - Averaging 13482.0162162162 Midmean - Empirical Distribution Function - Interpolation 13482.0162162162 Midmean - Closest Observation 13441.6263157895 Midmean - True Basic - Statistics Graphics Toolkit 13482.0162162162 Midmean - MS Excel (old versions) 13482.0162162162 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229442507kjism7no67cdovj/1uh7t1229442436.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229442507kjism7no67cdovj/1uh7t1229442436.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229442507kjism7no67cdovj/2kf981229442436.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229442507kjism7no67cdovj/2kf981229442436.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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