Centrummaten-Gemiddelde prijs badpak-Niels Braspennincx

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 13:02:26 -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/t1208718214q2zrzorltz07z4q.htm/, Retrieved Sun, 20 Apr 2008 21:03:36 +0200

User-defined keywords:

Dataseries X:

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38 38 37.93 38 38.02 38.02 38.02 37.96 37.96 37.99 38 38 38 38.01 38.06 38.02 38.05 38.05 38.05 38.05 38.03 37.98 38.03 38.04 38.04 38.08 38.14 38.37 38.49 38.55 38.55 38.55 38.48 38.51 38.48 38.48 38.48 38.43 38.43 38.45 38.48 38.47 38.47 38.42 38.55 38.56 38.57 38.57 38.57 38.57 38.62 38.73 38.74 38.68 38.69 38.69 38.61 38.77 38.78 38.81 38.81 38.81 38.76 38.93 38.95 38.97 38.97 38.96 38.92 38.95 38.95 38.97 38.97 39.05 39.08 38.83 38.86 38.87 38.87 38.75 38.86 38.93 38.96 38.95

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 38.4888095238095 0.0398870338141584 964.945393110365 Geometric Mean 38.4870921907245 Harmonic Mean 38.4853730393454 Quadratic Mean 38.4905249317778 Winsorized Mean ( 1 / 28 ) 38.4888095238095 0.0397660271120331 967.881689950439 Winsorized Mean ( 2 / 28 ) 38.4869047619048 0.0394635485419754 975.25200302168 Winsorized Mean ( 3 / 28 ) 38.4876190476190 0.0393505870953786 978.069754190252 Winsorized Mean ( 4 / 28 ) 38.4880952380952 0.0392772031323523 979.909264628697 Winsorized Mean ( 5 / 28 ) 38.4886904761905 0.0391870119989561 982.179771124569 Winsorized Mean ( 6 / 28 ) 38.4879761904762 0.0390821911342326 984.79576179044 Winsorized Mean ( 7 / 28 ) 38.4879761904762 0.0390821911342326 984.79576179044 Winsorized Mean ( 8 / 28 ) 38.4870238095238 0.0389446920009874 988.248252381813 Winsorized Mean ( 9 / 28 ) 38.4870238095238 0.0389446920009874 988.248252381813 Winsorized Mean ( 10 / 28 ) 38.4870238095238 0.0389446920009874 988.248252381813 Winsorized Mean ( 11 / 28 ) 38.4883333333333 0.0387486543483463 993.281805022886 Winsorized Mean ( 12 / 28 ) 38.4869047619048 0.0381319297626826 1009.30912758498 Winsorized Mean ( 13 / 28 ) 38.4869047619048 0.0381319297626826 1009.30912758498 Winsorized Mean ( 14 / 28 ) 38.4852380952381 0.0379000846167279 1015.43937129502 Winsorized Mean ( 15 / 28 ) 38.4763095238095 0.0367055470184680 1048.24236795737 Winsorized Mean ( 16 / 28 ) 38.4782142857143 0.0364216875027433 1056.4643464918 Winsorized Mean ( 17 / 28 ) 38.4761904761905 0.0361611364599047 1064.02049943460 Winsorized Mean ( 18 / 28 ) 38.4783333333333 0.0358439889959383 1073.49473122798 Winsorized Mean ( 19 / 28 ) 38.4715476190476 0.0349897509982188 1099.50904254809 Winsorized Mean ( 20 / 28 ) 38.4691666666667 0.0340552385866849 1129.61084001060 Winsorized Mean ( 21 / 28 ) 38.4691666666667 0.0340552385866849 1129.61084001060 Winsorized Mean ( 22 / 28 ) 38.4691666666667 0.0340552385866849 1129.61084001060 Winsorized Mean ( 23 / 28 ) 38.4609523809524 0.0330825126085362 1162.57651998985 Winsorized Mean ( 24 / 28 ) 38.4609523809524 0.0323246490018518 1189.83356567148 Winsorized Mean ( 25 / 28 ) 38.4639285714286 0.0310949621049114 1236.98264823913 Winsorized Mean ( 26 / 28 ) 38.4794047619048 0.0279985201592775 1374.3370914964 Winsorized Mean ( 27 / 28 ) 38.5501190476190 0.0174167094605809 2213.39852598846 Winsorized Mean ( 28 / 28 ) 38.5634523809524 0.0149684062455304 2576.32320691907 Trimmed Mean ( 1 / 28 ) 38.4884146341463 0.0396280772690983 971.241031271516 Trimmed Mean ( 2 / 28 ) 38.488 0.0394500966612539 975.612311687975 Trimmed Mean ( 3 / 28 ) 38.4885897435897 0.0394026848542764 976.801197327866 Trimmed Mean ( 4 / 28 ) 38.4889473684211 0.0393685148699511 977.65809798933 Trimmed Mean ( 5 / 28 ) 38.4891891891892 0.0393249954458751 978.746183001184 Trimmed Mean ( 6 / 28 ) 38.4893055555556 0.0392702039688246 980.11473498103 Trimmed Mean ( 7 / 28 ) 38.4895714285714 0.0392013624822827 981.84269605341 Trimmed Mean ( 8 / 28 ) 38.4898529411765 0.0390894455300444 984.661010645263 Trimmed Mean ( 9 / 28 ) 38.490303030303 0.0389542614447664 988.089662151054 Trimmed Mean ( 10 / 28 ) 38.49078125 0.0387620339017114 993.00210478121 Trimmed Mean ( 11 / 28 ) 38.4912903225806 0.0385014671892569 999.735675873696 Trimmed Mean ( 12 / 28 ) 38.4916666666667 0.0381945411743339 1007.77926591595 Trimmed Mean ( 13 / 28 ) 38.4922413793103 0.0379033405473583 1015.53691108614 Trimmed Mean ( 14 / 28 ) 38.4928571428571 0.0375159829884789 1026.03887934053 Trimmed Mean ( 15 / 28 ) 38.4937037037037 0.0370508709314399 1038.94193944681 Trimmed Mean ( 16 / 28 ) 38.4955769230769 0.0366523489064119 1050.28949226069 Trimmed Mean ( 17 / 28 ) 38.4974 0.0361717106736912 1064.29580694397 Trimmed Mean ( 18 / 28 ) 38.4995833333333 0.0355765062296494 1082.16312992668 Trimmed Mean ( 19 / 28 ) 38.5017391304348 0.0348499951106203 1104.78463506876 Trimmed Mean ( 20 / 28 ) 38.5047727272727 0.0340430777911309 1131.06026909542 Trimmed Mean ( 21 / 28 ) 38.5083333333333 0.0331485879208445 1161.68849862586 Trimmed Mean ( 22 / 28 ) 38.51225 0.0319303880259414 1206.13160005169 Trimmed Mean ( 23 / 28 ) 38.5165789473684 0.0302603128107882 1272.84140082110 Trimmed Mean ( 24 / 28 ) 38.5222222222222 0.028160850656544 1367.93531885978 Trimmed Mean ( 25 / 28 ) 38.5285294117647 0.0253816935199992 1517.96527609187 Trimmed Mean ( 26 / 28 ) 38.5353125 0.0216877788863727 1776.82153169744 Trimmed Mean ( 27 / 28 ) 38.5413333333333 0.0173915908688708 2216.09015666982 Trimmed Mean ( 28 / 28 ) 38.5403571428571 0.0160314022436814 2404.05402827737 Median 38.55 Midrange 38.505 Midmean - Weighted Average at Xnp 38.5047727272727 Midmean - Weighted Average at X(n+1)p 38.5047727272727 Midmean - Empirical Distribution Function 38.5047727272727 Midmean - Empirical Distribution Function - Averaging 38.5047727272727 Midmean - Empirical Distribution Function - Interpolation 38.5047727272727 Midmean - Closest Observation 38.5047727272727 Midmean - True Basic - Statistics Graphics Toolkit 38.5047727272727 Midmean - MS Excel (old versions) 38.5047727272727 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208718214q2zrzorltz07z4q/1jmsp1208718137.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208718214q2zrzorltz07z4q/1jmsp1208718137.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208718214q2zrzorltz07z4q/2rdva1208718137.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208718214q2zrzorltz07z4q/2rdva1208718137.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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