Centrummaten rode wijn

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 23 Oct 2009 05:49:02 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/23/t12562985906gvw8k5tzujxpox.htm/, Retrieved Fri, 23 Oct 2009 13:49:52 +0200

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/2009/Oct/23/t12562985906gvw8k5tzujxpox.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

2,12 2,12 2,13 2,14 2,15 2,15 2,16 2,17 2,17 2,18 2,17 2,17 2,18 2,17 2,18 2,18 2,18 2,17 2,17 2,18 2,17 2,18 2,17 2,17 2,17 2,17 2,17 2,17 2,17 2,17 2,17 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,18 2,19 2,19 2,19 2,2 2,2 2,21 2,21 2,21 2,2 2,21 2,2 2,21 2,21 2,22 2,22 2,23 2,24 2,24 2,25 2,25 2,32 2,36 2,37 2,37 2,37 2,38 2,38 2,41 2,42 2,43 2,44 2,44 2,44 2,43 2,43 2,43 2,42 2,42 2,42 2,42 2,42

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.23835294117647 0.010893997857664 205.466622118139 Geometric Mean 2.23619320310022 Harmonic Mean 2.23410061227542 Quadratic Mean 2.24057870675780 Winsorized Mean ( 1 / 28 ) 2.23835294117647 0.010893997857664 205.466622118139 Winsorized Mean ( 2 / 28 ) 2.23858823529412 0.0108647825451245 206.040776793887 Winsorized Mean ( 3 / 28 ) 2.23858823529412 0.0107481389714444 208.276822735694 Winsorized Mean ( 4 / 28 ) 2.23905882352941 0.0106991236707713 209.274973579962 Winsorized Mean ( 5 / 28 ) 2.23905882352941 0.0106991236707713 209.274973579963 Winsorized Mean ( 6 / 28 ) 2.23976470588235 0.0106326178432854 210.650353364932 Winsorized Mean ( 7 / 28 ) 2.23976470588235 0.0103901166011583 215.566849907408 Winsorized Mean ( 8 / 28 ) 2.23976470588235 0.0103901166011583 215.566849907408 Winsorized Mean ( 9 / 28 ) 2.23976470588235 0.0103901166011583 215.566849907408 Winsorized Mean ( 10 / 28 ) 2.23976470588235 0.0103901166011583 215.566849907408 Winsorized Mean ( 11 / 28 ) 2.23976470588235 0.0103901166011583 215.566849907408 Winsorized Mean ( 12 / 28 ) 2.23976470588235 0.0103901166011583 215.566849907408 Winsorized Mean ( 13 / 28 ) 2.23823529411765 0.0100769816612035 222.113661547573 Winsorized Mean ( 14 / 28 ) 2.23329411764706 0.00910010963595438 245.413979280354 Winsorized Mean ( 15 / 28 ) 2.23329411764706 0.00910010963595438 245.413979280354 Winsorized Mean ( 16 / 28 ) 2.23141176470588 0.0087417875685067 255.258063321603 Winsorized Mean ( 17 / 28 ) 2.23141176470588 0.0087417875685067 255.258063321602 Winsorized Mean ( 18 / 28 ) 2.23141176470588 0.0087417875685067 255.258063321602 Winsorized Mean ( 19 / 28 ) 2.22917647058824 0.00832163621311759 267.877183464753 Winsorized Mean ( 20 / 28 ) 2.21976470588235 0.00658488310075819 337.100093033811 Winsorized Mean ( 21 / 28 ) 2.20247058823529 0.00359701822652195 612.304539353118 Winsorized Mean ( 22 / 28 ) 2.20247058823529 0.00359701822652195 612.304539353118 Winsorized Mean ( 23 / 28 ) 2.19976470588235 0.00317984051970582 691.78460122455 Winsorized Mean ( 24 / 28 ) 2.20258823529412 0.00288991747324072 762.163022193211 Winsorized Mean ( 25 / 28 ) 2.19964705882353 0.00244518081350707 899.584622402065 Winsorized Mean ( 26 / 28 ) 2.19658823529412 0.00200526576524332 1095.41003161124 Winsorized Mean ( 27 / 28 ) 2.19658823529412 0.00200526576524332 1095.41003161124 Winsorized Mean ( 28 / 28 ) 2.19329411764706 0.00156456055431757 1401.85952636632 Trimmed Mean ( 1 / 28 ) 2.23734939759036 0.0107915961052413 207.323307485879 Trimmed Mean ( 2 / 28 ) 2.23629629629630 0.0106696240756154 209.594666170777 Trimmed Mean ( 3 / 28 ) 2.23506329113924 0.0105417569990547 212.019997362837 Trimmed Mean ( 4 / 28 ) 2.23376623376623 0.0104381768157638 213.999654651643 Trimmed Mean ( 5 / 28 ) 2.23226666666667 0.0103272112059012 216.153869826067 Trimmed Mean ( 6 / 28 ) 2.23068493150685 0.0101909634948292 218.888521447328 Trimmed Mean ( 7 / 28 ) 2.22887323943662 0.0100392575414163 222.015744714344 Trimmed Mean ( 8 / 28 ) 2.22695652173913 0.0099085854680293 224.750195567728 Trimmed Mean ( 9 / 28 ) 2.22492537313433 0.0097442955150670 228.331065051759 Trimmed Mean ( 10 / 28 ) 2.22276923076923 0.0095386553950524 233.027522088927 Trimmed Mean ( 11 / 28 ) 2.22047619047619 0.00928147920279624 239.237317884333 Trimmed Mean ( 12 / 28 ) 2.21803278688525 0.008958982646585 247.576412901159 Trimmed Mean ( 13 / 28 ) 2.21542372881356 0.00855183949402915 259.058151215345 Trimmed Mean ( 14 / 28 ) 2.21280701754386 0.00811012233777278 272.845084868540 Trimmed Mean ( 15 / 28 ) 2.21054545454545 0.00778247267457569 284.041531140484 Trimmed Mean ( 16 / 28 ) 2.20811320754717 0.00735802536581688 300.095894994516 Trimmed Mean ( 17 / 28 ) 2.20568627450980 0.00689560759290692 319.868299463365 Trimmed Mean ( 18 / 28 ) 2.20306122448980 0.00627599411883467 351.029842089601 Trimmed Mean ( 19 / 28 ) 2.20021276595745 0.00541086515883359 406.628644656845 Trimmed Mean ( 20 / 28 ) 2.19733333333333 0.00429234695990927 511.918853218655 Trimmed Mean ( 21 / 28 ) 2.19511627906977 0.0033670294590322 651.944482749111 Trimmed Mean ( 22 / 28 ) 2.19439024390244 0.00320153889231422 685.417331387229 Trimmed Mean ( 23 / 28 ) 2.19358974358974 0.00297282290830681 737.881068347632 Trimmed Mean ( 24 / 28 ) 2.19297297297297 0.00279061234265469 785.839344094213 Trimmed Mean ( 25 / 28 ) 2.192 0.00258632473410669 847.534716384758 Trimmed Mean ( 26 / 28 ) 2.19121212121212 0.00245248697821797 893.465343821847 Trimmed Mean ( 27 / 28 ) 2.19064516129032 0.00240677734253756 910.198514242551 Trimmed Mean ( 28 / 28 ) 2.19 0.00232781425629766 940.7967126566 Median 2.18 Midrange 2.28 Midmean - Weighted Average at Xnp 2.18894736842105 Midmean - Weighted Average at X(n+1)p 2.18894736842105 Midmean - Empirical Distribution Function 2.18894736842105 Midmean - Empirical Distribution Function - Averaging 2.18894736842105 Midmean - Empirical Distribution Function - Interpolation 2.18894736842105 Midmean - Closest Observation 2.18894736842105 Midmean - True Basic - Statistics Graphics Toolkit 2.18894736842105 Midmean - MS Excel (old versions) 2.18894736842105 Number of observations 85

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/23/t12562985906gvw8k5tzujxpox/1dqsi1256298539.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/23/t12562985906gvw8k5tzujxpox/1dqsi1256298539.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/23/t12562985906gvw8k5tzujxpox/244ll1256298539.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/23/t12562985906gvw8k5tzujxpox/244ll1256298539.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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