Toon Raeman - Opg.5 - centrummaten eigen reeks

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

Title produced by software: Central Tendency

Date of computation: Sun, 17 Aug 2008 05:18:56 -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/Aug/17/t12189721842bwfp4sv473m9u1.htm/, Retrieved Sun, 17 Aug 2008 11:23:04 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

12,11 11,42 11,71 12,04 12,21 12 12,36 12,32 12,96 12,79 13,19 12,34 13,25 12,54 12,77 12,96 13 13,61 13,8 14,16 14,27 14,69 15,01 15,09 15,14 14,2 13,83 14,31 14,04 14,9 14,92 15,36 15,5 15,65 16,18 15,44 15,58 15,24 15,33 16,07 15,82 15,87 15,72 17,07 16,83 17,52 17,76 17,36 17,95 16,71 17,14 16,72 17,26 17,24 17,69 18,13 18,08 18,18 18,18 17,64 17,89 16,82 16,61 16,66 17,02 16,91 17,18 18,06 17,58 17,48 17,54 17,44 17,79 16,79 16,19 16,62 16,39 16,54 17,26 18 17,29 18,16 17,82 17,48 18,31 17,04 17,03 16,97 17,11 17,12 17,69 18,5 18,27 18,45 18,35 18,03

Text written by user:

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 15.8911458333333 0.204876667531811 77.5644490159718 Geometric Mean 15.7567057273771 Harmonic Mean 15.6134909014067 Quadratic Mean 16.0161196468329 Winsorized Mean ( 1 / 32 ) 15.8936458333333 0.204134572475222 77.8586676456409 Winsorized Mean ( 2 / 32 ) 15.8976041666667 0.202600946508483 78.4675710584652 Winsorized Mean ( 3 / 32 ) 15.8976041666667 0.202190729002480 78.6267710942954 Winsorized Mean ( 4 / 32 ) 15.8988541666667 0.201401115749779 78.941241747734 Winsorized Mean ( 5 / 32 ) 15.899375 0.199807133568849 79.5736103912497 Winsorized Mean ( 6 / 32 ) 15.90625 0.19848517610033 80.1382265039266 Winsorized Mean ( 7 / 32 ) 15.90625 0.198032994437707 80.3212113474527 Winsorized Mean ( 8 / 32 ) 15.9054166666667 0.197419477070781 80.5666031673465 Winsorized Mean ( 9 / 32 ) 15.9176041666667 0.193722068999278 82.1672215710538 Winsorized Mean ( 10 / 32 ) 15.9394791666667 0.18916444680232 84.2625526948184 Winsorized Mean ( 11 / 32 ) 15.9383333333333 0.188357027697511 84.6176727683835 Winsorized Mean ( 12 / 32 ) 15.9558333333333 0.184230182744083 86.6081393161176 Winsorized Mean ( 13 / 32 ) 15.9490625 0.18344606251871 86.9414272567084 Winsorized Mean ( 14 / 32 ) 15.9461458333333 0.181451589031615 87.880993043026 Winsorized Mean ( 15 / 32 ) 15.9648958333333 0.175212652425539 91.1172544466675 Winsorized Mean ( 16 / 32 ) 15.9698958333333 0.172996076341754 92.3136302917346 Winsorized Mean ( 17 / 32 ) 16.0283333333333 0.16211416181811 98.8706548124828 Winsorized Mean ( 18 / 32 ) 16.0508333333333 0.155126905226483 103.469048840363 Winsorized Mean ( 19 / 32 ) 16.0567708333333 0.154222263194163 104.114480625396 Winsorized Mean ( 20 / 32 ) 16.0901041666667 0.146512341165693 109.820811261695 Winsorized Mean ( 21 / 32 ) 16.1032291666667 0.141224244258852 114.025953908812 Winsorized Mean ( 22 / 32 ) 16.1032291666667 0.138895667552050 115.937591506460 Winsorized Mean ( 23 / 32 ) 16.1152083333333 0.135966728641659 118.523174708461 Winsorized Mean ( 24 / 32 ) 16.1152083333333 0.133458464788976 120.750739631350 Winsorized Mean ( 25 / 32 ) 16.2141666666667 0.119762526966898 135.385976542964 Winsorized Mean ( 26 / 32 ) 16.2602083333333 0.111073606380439 146.391288292561 Winsorized Mean ( 27 / 32 ) 16.2433333333333 0.107863590212672 150.591439625797 Winsorized Mean ( 28 / 32 ) 16.2491666666667 0.102287934955335 158.857119109521 Winsorized Mean ( 29 / 32 ) 16.2642708333333 0.0982578224187974 165.526473444641 Winsorized Mean ( 30 / 32 ) 16.2798958333333 0.0963015064728484 169.051310094753 Winsorized Mean ( 31 / 32 ) 16.3057291666667 0.091619415029477 177.97242169054 Winsorized Mean ( 32 / 32 ) 16.3157291666667 0.0858350040024345 190.082465263285 Trimmed Mean ( 1 / 32 ) 15.9109574468085 0.2017915678614 78.8484752630344 Trimmed Mean ( 2 / 32 ) 15.9290217391304 0.199092545939332 80.0081271952007 Trimmed Mean ( 3 / 32 ) 15.9457777777778 0.196893602184576 80.9867745871681 Trimmed Mean ( 4 / 32 ) 15.9632954545455 0.194508176058428 82.070048560582 Trimmed Mean ( 5 / 32 ) 15.9812790697674 0.191992988679526 83.2388681466038 Trimmed Mean ( 6 / 32 ) 16 0.189501338557210 84.4321212811363 Trimmed Mean ( 7 / 32 ) 16.0182926829268 0.186912810748709 85.6992766775214 Trimmed Mean ( 8 / 32 ) 16.0375 0.183970493300049 87.1743055765114 Trimmed Mean ( 9 / 32 ) 16.0578205128205 0.180633495753349 88.8972471348675 Trimmed Mean ( 10 / 32 ) 16.0775 0.177444246247422 90.6059246214278 Trimmed Mean ( 11 / 32 ) 16.0954054054054 0.174546133736229 92.212901316557 Trimmed Mean ( 12 / 32 ) 16.1144444444444 0.171231374012934 94.109181435566 Trimmed Mean ( 13 / 32 ) 16.1325714285714 0.168020959664918 96.0152320326251 Trimmed Mean ( 14 / 32 ) 16.1525 0.164282484263068 98.3214983170983 Trimmed Mean ( 15 / 32 ) 16.1739393939394 0.160108628449137 101.018536918374 Trimmed Mean ( 16 / 32 ) 16.19484375 0.156166087338761 103.702692601049 Trimmed Mean ( 17 / 32 ) 16.2166129032258 0.151744473273781 106.867898074728 Trimmed Mean ( 18 / 32 ) 16.2343333333333 0.148333942739813 109.444494183029 Trimmed Mean ( 19 / 32 ) 16.2512068965517 0.145333768512992 111.819896111061 Trimmed Mean ( 20 / 32 ) 16.26875 0.141741731131505 114.777418549419 Trimmed Mean ( 21 / 32 ) 16.2846296296296 0.138649448859237 117.451816531651 Trimmed Mean ( 22 / 32 ) 16.3005769230769 0.135668951361818 120.149649270927 Trimmed Mean ( 23 / 32 ) 16.3178 0.132248155729589 123.38773202528 Trimmed Mean ( 24 / 32 ) 16.3354166666667 0.128403646000207 127.219258763418 Trimmed Mean ( 25 / 32 ) 16.3545652173913 0.123879599690553 132.019842316608 Trimmed Mean ( 26 / 32 ) 16.3668181818182 0.121047564920921 135.209809404348 Trimmed Mean ( 27 / 32 ) 16.3761904761905 0.119074027268390 137.529491962836 Trimmed Mean ( 28 / 32 ) 16.388 0.116909015686208 140.177384129096 Trimmed Mean ( 29 / 32 ) 16.4005263157895 0.115027331385354 142.579386292515 Trimmed Mean ( 30 / 32 ) 16.4130555555556 0.113183948778186 145.012218894407 Trimmed Mean ( 31 / 32 ) 16.4255882352941 0.110895071068329 148.118289451958 Trimmed Mean ( 32 / 32 ) 16.4371875 0.108717073598096 151.192328453990 Median 16.64 Midrange 14.96 Midmean - Weighted Average at Xnp 16.2932653061224 Midmean - Weighted Average at X(n+1)p 16.3354166666667 Midmean - Empirical Distribution Function 16.2932653061224 Midmean - Empirical Distribution Function - Averaging 16.3354166666667 Midmean - Empirical Distribution Function - Interpolation 16.3354166666667 Midmean - Closest Observation 16.2932653061224 Midmean - True Basic - Statistics Graphics Toolkit 16.3354166666667 Midmean - MS Excel (old versions) 16.3178 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12189721842bwfp4sv473m9u1/17c051218971930.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12189721842bwfp4sv473m9u1/17c051218971930.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12189721842bwfp4sv473m9u1/2p7xc1218971930.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12189721842bwfp4sv473m9u1/2p7xc1218971930.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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