Centrummaten eigen reeks Katrien Devillé

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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 09:07:05 -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/21/t120879053774ljo2sgy8bpzfd.htm/, Retrieved Mon, 21 Apr 2008 17:09:00 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

20,18 20,19 20,3 20,47 20,47 20,46 20,46 20,46 20,52 20,64 20,65 20,66 20,66 20,66 20,67 20,71 20,73 20,73 20,74 20,74 20,75 20,75 20,77 20,78 20,78 20,8 20,84 20,85 20,86 20,86 20,86 20,86 20,9 20,92 20,95 20,95 20,95 20,96 21,1 21,18 21,19 21,19 21,19 21,19 21,19 21,21 21,22 21,22 21,22 21,23 21,41 21,42 21,43 21,44 21,44 21,44 21,48 21,53 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,57 21,6 21,61 21,6 21,6 21,71 21,75 21,84 21,85 21,92 21,92 21,93 22 22 21,99 22,01 22,01 22,06 22,03 22,05 22,05 22,06 22,06 22,13 22,06 22,25 22,28 22,18

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 21.2701041666667 0.0559057192708016 380.463831681272 Geometric Mean 21.2631244685508 Harmonic Mean 21.2561460885451 Quadratic Mean 21.2770827172884 Winsorized Mean ( 1 / 32 ) 21.2698958333333 0.0558258363895175 381.004517064919 Winsorized Mean ( 2 / 32 ) 21.2707291666667 0.0551185414706552 385.908781312566 Winsorized Mean ( 3 / 32 ) 21.2741666666667 0.0539914846004138 394.028184705697 Winsorized Mean ( 4 / 32 ) 21.27125 0.053521853628116 397.431115667224 Winsorized Mean ( 5 / 32 ) 21.27125 0.053521853628116 397.431115667224 Winsorized Mean ( 6 / 32 ) 21.271875 0.0534226183494949 398.181063699232 Winsorized Mean ( 7 / 32 ) 21.271875 0.0534226183494949 398.181063699232 Winsorized Mean ( 8 / 32 ) 21.2752083333333 0.0526495320714172 404.091119071567 Winsorized Mean ( 9 / 32 ) 21.2864583333333 0.0510488627222382 416.982028554779 Winsorized Mean ( 10 / 32 ) 21.2854166666667 0.0505851541624362 420.783864734625 Winsorized Mean ( 11 / 32 ) 21.2842708333333 0.0500818945100122 424.98933080653 Winsorized Mean ( 12 / 32 ) 21.2842708333333 0.0500818945100122 424.98933080653 Winsorized Mean ( 13 / 32 ) 21.2829166666667 0.0498761441118095 426.715357525550 Winsorized Mean ( 14 / 32 ) 21.284375 0.0496853724856228 428.383122339657 Winsorized Mean ( 15 / 32 ) 21.2890625 0.0486499937174316 437.596408000603 Winsorized Mean ( 16 / 32 ) 21.2823958333333 0.0467458002597294 455.279313116557 Winsorized Mean ( 17 / 32 ) 21.280625 0.0464884942613139 457.761115694147 Winsorized Mean ( 18 / 32 ) 21.2825 0.0462558673376460 460.103792771797 Winsorized Mean ( 19 / 32 ) 21.2686458333333 0.044292840247445 480.18247903080 Winsorized Mean ( 20 / 32 ) 21.2686458333333 0.0437448292161552 486.19793960651 Winsorized Mean ( 21 / 32 ) 21.2489583333333 0.0411262708881287 516.676029079674 Winsorized Mean ( 22 / 32 ) 21.244375 0.0393844669766533 539.409991573416 Winsorized Mean ( 23 / 32 ) 21.2228125 0.0362344047291322 585.708876926492 Winsorized Mean ( 24 / 32 ) 21.2203125 0.0359548489778768 590.193342574098 Winsorized Mean ( 25 / 32 ) 21.2255208333333 0.0352885566759735 601.484527356283 Winsorized Mean ( 26 / 32 ) 21.2363541666667 0.0339346378285388 625.801703674204 Winsorized Mean ( 27 / 32 ) 21.2307291666667 0.0326515511008426 650.221151855748 Winsorized Mean ( 28 / 32 ) 21.2248958333333 0.0313521994778349 676.982673842028 Winsorized Mean ( 29 / 32 ) 21.2248958333333 0.0313521994778349 676.982673842028 Winsorized Mean ( 30 / 32 ) 21.2248958333333 0.0313521994778349 676.982673842028 Winsorized Mean ( 31 / 32 ) 21.2248958333333 0.0313521994778349 676.982673842028 Winsorized Mean ( 32 / 32 ) 21.2382291666667 0.0297367819639523 714.207381027718 Trimmed Mean ( 1 / 32 ) 21.2709574468085 0.0548451093983114 387.83690433232 Trimmed Mean ( 2 / 32 ) 21.2720652173913 0.05372941400547 395.910984907181 Trimmed Mean ( 3 / 32 ) 21.2727777777778 0.0528812836147962 402.274232462573 Trimmed Mean ( 4 / 32 ) 21.2722727272727 0.0523780684062209 406.129385343012 Trimmed Mean ( 5 / 32 ) 21.2725581395349 0.0519439311648308 409.529230123763 Trimmed Mean ( 6 / 32 ) 21.2728571428571 0.0514328741745676 413.604284890929 Trimmed Mean ( 7 / 32 ) 21.2730487804878 0.0508570594960411 418.290970639853 Trimmed Mean ( 8 / 32 ) 21.27325 0.0501815611781706 423.925631258639 Trimmed Mean ( 9 / 32 ) 21.2729487179487 0.0495471026777706 429.347985416973 Trimmed Mean ( 10 / 32 ) 21.2710526315789 0.0490962459519496 433.252119773004 Trimmed Mean ( 11 / 32 ) 21.2691891891892 0.0486347320586052 437.325102635698 Trimmed Mean ( 12 / 32 ) 21.2673611111111 0.0481614204526186 441.585005409756 Trimmed Mean ( 13 / 32 ) 21.2654285714286 0.0475850271848797 446.893273567063 Trimmed Mean ( 14 / 32 ) 21.2635294117647 0.0469208909191635 453.178296388235 Trimmed Mean ( 15 / 32 ) 21.2613636363636 0.0461460569467349 460.74063621308 Trimmed Mean ( 16 / 32 ) 21.25859375 0.0453709726379116 468.550540444807 Trimmed Mean ( 17 / 32 ) 21.2562903225806 0.0447374583939675 475.13406182786 Trimmed Mean ( 18 / 32 ) 21.254 0.0439942215003713 483.108901013753 Trimmed Mean ( 19 / 32 ) 21.2513793103448 0.0431078279686598 492.981908663897 Trimmed Mean ( 20 / 32 ) 21.2498214285714 0.0423478875041812 501.791770049293 Trimmed Mean ( 21 / 32 ) 21.2481481481481 0.041483727602162 512.204408242252 Trimmed Mean ( 22 / 32 ) 21.2480769230769 0.0408488720964105 520.163124037495 Trimmed Mean ( 23 / 32 ) 21.2484 0.0403215241046572 526.974127883866 Trimmed Mean ( 24 / 32 ) 21.250625 0.0401287889552399 529.560586134388 Trimmed Mean ( 25 / 32 ) 21.2532608695652 0.0398609350101898 533.185206622277 Trimmed Mean ( 26 / 32 ) 21.2556818181818 0.0395741038600881 537.11088173544 Trimmed Mean ( 27 / 32 ) 21.2573809523810 0.0393885606942768 539.684125992186 Trimmed Mean ( 28 / 32 ) 21.25975 0.0392860768381539 541.152278645266 Trimmed Mean ( 29 / 32 ) 21.2628947368421 0.0392767253148244 541.361189518943 Trimmed Mean ( 30 / 32 ) 21.2663888888889 0.0391317529854051 543.456075091259 Trimmed Mean ( 31 / 32 ) 21.2702941176471 0.0387976268044035 548.236989465369 Trimmed Mean ( 32 / 32 ) 21.2746875 0.0381951281911754 557.000028734432 Median 21.22 Midrange 21.23 Midmean - Weighted Average at Xnp 21.2410204081633 Midmean - Weighted Average at X(n+1)p 21.2410204081633 Midmean - Empirical Distribution Function 21.2410204081633 Midmean - Empirical Distribution Function - Averaging 21.2410204081633 Midmean - Empirical Distribution Function - Interpolation 21.2410204081633 Midmean - Closest Observation 21.2410204081633 Midmean - True Basic - Statistics Graphics Toolkit 21.2410204081633 Midmean - MS Excel (old versions) 21.2484 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t120879053774ljo2sgy8bpzfd/1os0e1208790421.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t120879053774ljo2sgy8bpzfd/1os0e1208790421.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t120879053774ljo2sgy8bpzfd/2o72j1208790421.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t120879053774ljo2sgy8bpzfd/2o72j1208790421.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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Software written by Ed van Stee & Patrick Wessa

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