centrummaten eigen gegevens_Jan De Cleermaecker

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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 03:12:13 -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/Apr/20/t1208682788nfyzkxachqa3o5q.htm/, Retrieved Sun, 20 Apr 2008 11:13:08 +0200

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Dataseries X:

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68,4 70,6 83,9 90,1 90,6 87,1 90,8 94,1 99,8 96,8 87 96,3 107,1 115,2 106,1 89,5 91,3 97,6 100,7 104,6 94,7 101,8 102,5 105,3 110,3 109,8 117,3 118,8 131,3 125,9 133,1 147 145,8 164,4 149,8 137,7 151,7 156,8 180 180,4 170,4 191,6 199,5 218,2 217,5 205 194 199,3 219,3 211,1 215,2 240,2 242,2 240,7 255,4 253 218,2 203,7 205,6 215,6 188,5 202,9 214 230,3 230 241 259,6 247,8 270,3 289,7 322,7 315 320,2

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 166.845205479452 7.93300022349848 21.0317913499154 Geometric Mean 153.322695450361 Harmonic Mean 140.699944865588 Quadratic Mean 179.912373267640 Winsorized Mean ( 1 / 24 ) 166.841095890411 7.91858107965885 21.0695696883107 Winsorized Mean ( 2 / 24 ) 167.06301369863 7.82303084935107 21.3552799312415 Winsorized Mean ( 3 / 24 ) 166.150684931507 7.5493163285991 22.008706179403 Winsorized Mean ( 4 / 24 ) 165.093150684932 7.32139629556889 22.5494077932717 Winsorized Mean ( 5 / 24 ) 164.524657534247 7.15645491559805 22.9896868595724 Winsorized Mean ( 6 / 24 ) 164.228767123288 7.08658761652047 23.1745906507150 Winsorized Mean ( 7 / 24 ) 164.046575342466 7.0388714919713 23.3058062687437 Winsorized Mean ( 8 / 24 ) 163.498630136986 6.93757539845508 23.5671139766489 Winsorized Mean ( 9 / 24 ) 162.869863013699 6.81449672536299 23.9004976563435 Winsorized Mean ( 10 / 24 ) 163.089041095890 6.7327242597294 24.2233358748076 Winsorized Mean ( 11 / 24 ) 163.134246575342 6.71262957500114 24.3025843676641 Winsorized Mean ( 12 / 24 ) 163.315068493151 6.66245376909975 24.5127507301590 Winsorized Mean ( 13 / 24 ) 161.641095890411 6.37662888003769 25.3489890867626 Winsorized Mean ( 14 / 24 ) 161.73698630137 6.34642767564532 25.4847285067224 Winsorized Mean ( 15 / 24 ) 159.990410958904 5.96665109446182 26.8141053374824 Winsorized Mean ( 16 / 24 ) 159.946575342466 5.90593214990906 27.0823591065008 Winsorized Mean ( 17 / 24 ) 160.202739726027 5.8703881709635 27.289973858702 Winsorized Mean ( 18 / 24 ) 160.202739726027 5.8229486731716 27.5123049708713 Winsorized Mean ( 19 / 24 ) 160.254794520548 5.68089170797837 28.2094436504541 Winsorized Mean ( 20 / 24 ) 160.33698630137 5.6400305718165 28.4283895733795 Winsorized Mean ( 21 / 24 ) 160.221917808219 5.56238736023156 28.8045235672959 Winsorized Mean ( 22 / 24 ) 159.649315068493 5.40521413921267 29.5361684027097 Winsorized Mean ( 23 / 24 ) 158.767123287671 5.0647264274951 31.3476207571183 Winsorized Mean ( 24 / 24 ) 158.734246575342 5.01737097377711 31.6369364364234 Trimmed Mean ( 1 / 24 ) 166.03661971831 7.7270408253904 21.4877368284024 Trimmed Mean ( 2 / 24 ) 165.185507246377 7.49850944988411 22.0291123656488 Trimmed Mean ( 3 / 24 ) 164.162686567164 7.28526912678971 22.5335102533821 Trimmed Mean ( 4 / 24 ) 163.418461538462 7.1546884481395 22.8407515886952 Trimmed Mean ( 5 / 24 ) 162.933333333333 7.07804492201588 23.0195393118427 Trimmed Mean ( 6 / 24 ) 162.552459016393 7.03115339532708 23.1188895870806 Trimmed Mean ( 7 / 24 ) 162.206779661017 6.98714644581956 23.2150250347287 Trimmed Mean ( 8 / 24 ) 161.870175438596 6.93880743732902 23.3282414738556 Trimmed Mean ( 9 / 24 ) 161.6 6.89621132504875 23.4331566106492 Trimmed Mean ( 10 / 24 ) 161.405660377358 6.8629018979417 23.5185731601040 Trimmed Mean ( 11 / 24 ) 161.164705882353 6.8295131302538 23.5982716203320 Trimmed Mean ( 12 / 24 ) 160.897959183673 6.78229330420404 23.7232381389257 Trimmed Mean ( 13 / 24 ) 160.585106382979 6.7231674363145 23.8853349859465 Trimmed Mean ( 14 / 24 ) 160.453333333333 6.69671380287195 23.9600105449514 Trimmed Mean ( 15 / 24 ) 160.297674418605 6.6558623593941 24.0836822883454 Trimmed Mean ( 16 / 24 ) 160.334146341463 6.66559295091363 24.0539960243877 Trimmed Mean ( 17 / 24 ) 160.379487179487 6.67142088862944 24.0397795097642 Trimmed Mean ( 18 / 24 ) 160.4 6.66587044794818 24.0628738965926 Trimmed Mean ( 19 / 24 ) 160.422857142857 6.64672925911215 24.1356087917873 Trimmed Mean ( 20 / 24 ) 160.442424242424 6.6295582236366 24.2010732586061 Trimmed Mean ( 21 / 24 ) 160.454838709677 6.58878297165113 24.3527278709968 Trimmed Mean ( 22 / 24 ) 160.482758620690 6.5231362945578 24.6020857719283 Trimmed Mean ( 23 / 24 ) 160.585185185185 6.4427739590843 24.9248516562901 Trimmed Mean ( 24 / 24 ) 160.816 6.3943664789146 25.1496376584436 Median 156.8 Midrange 195.55 Midmean - Weighted Average at Xnp 158.813888888889 Midmean - Weighted Average at X(n+1)p 160.4 Midmean - Empirical Distribution Function 160.4 Midmean - Empirical Distribution Function - Averaging 160.4 Midmean - Empirical Distribution Function - Interpolation 160.4 Midmean - Closest Observation 158.857894736842 Midmean - True Basic - Statistics Graphics Toolkit 160.4 Midmean - MS Excel (old versions) 160.4 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208682788nfyzkxachqa3o5q/1lluy1208682728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208682788nfyzkxachqa3o5q/1lluy1208682728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208682788nfyzkxachqa3o5q/24q4t1208682728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208682788nfyzkxachqa3o5q/24q4t1208682728.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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