Central Tendency Vlaams Gewest

*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: Sun, 19 Oct 2008 18:29:52 -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/20/t12244626545qe317i6wx510qc.htm/, Retrieved Mon, 20 Oct 2008 00:30:54 +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/20/t12244626545qe317i6wx510qc.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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12055 12113 9617 12646 13581 12162 10970 11880 11888 12927 12300 12093 12381 12197 9455 13168 13428 11981 11885 11692 12234 14341 13131 12421 14286 12865 11160 14316 14389 14014 13419 12770 13316 15333 14243 13824 14963 13203 12199 15509 14200 15170 14058 13786 14148 16542 13588 15582 15803 14131 12923 15612 16034 16037 14038 15331 15038 17402 14993 16044 16930 15921 14417 15961 17852 16484 14216 17430 17840 17629

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 13964.2142857143 227.086265102680 61.4929937722134 Geometric Mean 13835.3086755969 Harmonic Mean 13704.4579260849 Quadratic Mean 14091.0427034847 Winsorized Mean ( 1 / 23 ) 13966.3571428571 226.388535396314 61.6919806403084 Winsorized Mean ( 2 / 23 ) 13998.9857142857 215.551536297830 64.9449591254276 Winsorized Mean ( 3 / 23 ) 13998.6 211.889613825702 66.065531704235 Winsorized Mean ( 4 / 23 ) 14027.4 206.057828623569 68.0750646248223 Winsorized Mean ( 5 / 23 ) 14007.1142857143 196.250644173866 71.3735964774968 Winsorized Mean ( 6 / 23 ) 13974.2857142857 189.319110300552 73.8133920664477 Winsorized Mean ( 7 / 23 ) 13968.7857142857 188.139134996218 74.2471028931143 Winsorized Mean ( 8 / 23 ) 13929.1285714286 177.204470592892 78.6048372528323 Winsorized Mean ( 9 / 23 ) 13937.7428571429 175.551204902555 79.3941737106243 Winsorized Mean ( 10 / 23 ) 13942.7428571429 174.63832449757 79.8378185158142 Winsorized Mean ( 11 / 23 ) 13934.4142857143 172.182246715504 80.9282870419157 Winsorized Mean ( 12 / 23 ) 13935.9571428571 169.736140907929 82.1036525769516 Winsorized Mean ( 13 / 23 ) 13920.5428571429 165.083528246862 84.3242387958078 Winsorized Mean ( 14 / 23 ) 13882.7428571429 158.84989813976 87.395352592096 Winsorized Mean ( 15 / 23 ) 13883.8142857143 156.689565692940 88.6071400116199 Winsorized Mean ( 16 / 23 ) 13882.2142857143 151.792421042914 91.4552531037739 Winsorized Mean ( 17 / 23 ) 13859.1428571429 142.294492815414 97.3976053670683 Winsorized Mean ( 18 / 23 ) 13868.9142857143 140.675717344744 98.5878341158672 Winsorized Mean ( 19 / 23 ) 13886.2857142857 125.185236071893 110.925905881672 Winsorized Mean ( 20 / 23 ) 13884 114.586658374493 121.165938486697 Winsorized Mean ( 21 / 23 ) 13899 108.641883264107 127.934085662080 Winsorized Mean ( 22 / 23 ) 13907.8 104.766637254297 132.750275894052 Winsorized Mean ( 23 / 23 ) 13729.7142857143 80.0720771135243 171.466943042437 Trimmed Mean ( 1 / 23 ) 13973.3529411765 216.535849826736 64.5313602914132 Trimmed Mean ( 2 / 23 ) 13980.7727272727 204.659188866820 68.3124603624351 Trimmed Mean ( 3 / 23 ) 13970.8125 197.521618109350 70.7305490595244 Trimmed Mean ( 4 / 23 ) 13960.3548387097 190.627984848751 73.2335016277184 Trimmed Mean ( 5 / 23 ) 13940.8 184.437538306938 75.5854807430793 Trimmed Mean ( 6 / 23 ) 13924.7931034483 180.091925103178 77.3204745047312 Trimmed Mean ( 7 / 23 ) 13914.4821428571 176.737526408388 78.7296417779716 Trimmed Mean ( 8 / 23 ) 13904.4259259259 172.834347891897 80.4494366746057 Trimmed Mean ( 9 / 23 ) 13900.2692307692 170.632967032898 81.4629756047628 Trimmed Mean ( 10 / 23 ) 13894.44 168.113494608219 82.6491652700478 Trimmed Mean ( 11 / 23 ) 13887.3958333333 164.996474654966 84.1678336605319 Trimmed Mean ( 12 / 23 ) 13880.8913043478 161.464784238063 85.9685371633847 Trimmed Mean ( 13 / 23 ) 13873.5909090909 157.356160426892 88.1668113371172 Trimmed Mean ( 14 / 23 ) 13867.5714285714 153.004445073918 90.635088554923 Trimmed Mean ( 15 / 23 ) 13865.675 148.680811909702 93.2579989435422 Trimmed Mean ( 16 / 23 ) 13863.4473684211 143.312298607779 96.7359221999704 Trimmed Mean ( 17 / 23 ) 13861.1666666667 137.219014485996 101.014911953629 Trimmed Mean ( 18 / 23 ) 13861.4117647059 131.383099850350 105.503765556563 Trimmed Mean ( 19 / 23 ) 13860.5 123.510978028467 112.220793821303 Trimmed Mean ( 20 / 23 ) 13857.3333333333 117.163902617779 118.273060419810 Trimmed Mean ( 21 / 23 ) 13854 111.306823666427 124.466762626511 Trimmed Mean ( 22 / 23 ) 13848.2307692308 104.439416486192 132.595826701709 Trimmed Mean ( 23 / 23 ) 13840.3333333333 95.0750593384646 145.572702553486 Median 14026 Midrange 13653.5 Midmean - Weighted Average at Xnp 13819.1142857143 Midmean - Weighted Average at X(n+1)p 13861.1666666667 Midmean - Empirical Distribution Function 13861.1666666667 Midmean - Empirical Distribution Function - Averaging 13861.1666666667 Midmean - Empirical Distribution Function - Interpolation 13861.4117647059 Midmean - Closest Observation 13861.1666666667 Midmean - True Basic - Statistics Graphics Toolkit 13861.1666666667 Midmean - MS Excel (old versions) 13861.1666666667 Number of observations 70

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t12244626545qe317i6wx510qc/1alyo1224462586.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t12244626545qe317i6wx510qc/1alyo1224462586.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t12244626545qe317i6wx510qc/2auvb1224462586.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t12244626545qe317i6wx510qc/2auvb1224462586.ps (open in new window)

Parameters (Session):

par1 = grey ; par2 = grey ; par3 = TRUE ; par4 = Totaal ; par5 = Waals Gewest ;

Parameters (R input):

par1 = grey ; par2 = grey ; par3 = TRUE ; par4 = Totaal ; par5 = Waals Gewest ;

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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