Centrummaten eigen reeks Dimitri Troquay

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

Title produced by software: Central Tendency

Date of computation: Sat, 19 Apr 2008 12:34:25 -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/19/t1208630145h22lrjhja865326.htm/, Retrieved Sat, 19 Apr 2008 20:35:47 +0200

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Dataseries X:

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8,16 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 9.25588235294118 0.0665574653496633 139.066028195558 Geometric Mean 9.23580095264941 Harmonic Mean 9.21577480600567 Quadratic Mean 9.27596191301822 Winsorized Mean ( 1 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 2 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 3 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 4 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 5 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 6 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 7 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 8 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 9 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 10 / 28 ) 9.25905882352941 0.0660083653830615 140.270990953904 Winsorized Mean ( 11 / 28 ) 9.22023529411765 0.0600669506184484 153.499307009699 Winsorized Mean ( 12 / 28 ) 9.22023529411765 0.0600669506184484 153.499307009699 Winsorized Mean ( 13 / 28 ) 9.22023529411765 0.0600669506184484 153.499307009699 Winsorized Mean ( 14 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 15 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 16 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 17 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 18 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 19 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 20 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 21 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 22 / 28 ) 9.26141176470588 0.0541817547461495 170.932296454722 Winsorized Mean ( 23 / 28 ) 9.18023529411765 0.0437365350133554 209.898550292436 Winsorized Mean ( 24 / 28 ) 9.18023529411765 0.0437365350133554 209.898550292436 Winsorized Mean ( 25 / 28 ) 9.18023529411765 0.0437365350133554 209.898550292436 Winsorized Mean ( 26 / 28 ) 9.25364705882353 0.0344109483012639 268.915781623015 Winsorized Mean ( 27 / 28 ) 9.25364705882353 0.0344109483012639 268.915781623015 Winsorized Mean ( 28 / 28 ) 9.25364705882353 0.0344109483012639 268.915781623015 Trimmed Mean ( 1 / 28 ) 9.2577108433735 0.0658773661211838 140.529462370180 Trimmed Mean ( 2 / 28 ) 9.2562962962963 0.0656915830817883 140.905362027459 Trimmed Mean ( 3 / 28 ) 9.25481012658228 0.0654425577098501 141.418832797076 Trimmed Mean ( 4 / 28 ) 9.25324675324675 0.0651202792604976 142.094703191174 Trimmed Mean ( 5 / 28 ) 9.2516 0.0647128209027329 142.963942398766 Trimmed Mean ( 6 / 28 ) 9.24986301369863 0.0642058657325833 144.065700355544 Trimmed Mean ( 7 / 28 ) 9.24802816901408 0.0635820798179507 145.450230560139 Trimmed Mean ( 8 / 28 ) 9.24608695652174 0.0628202680514873 147.183182168909 Trimmed Mean ( 9 / 28 ) 9.24402985074627 0.0618942137824765 149.352084562118 Trimmed Mean ( 10 / 28 ) 9.24184615384615 0.0607710442767377 152.076474311695 Trimmed Mean ( 11 / 28 ) 9.23952380952381 0.0594088598212856 155.524341610296 Trimmed Mean ( 12 / 28 ) 9.24196721311475 0.0588922419079717 156.930130585906 Trimmed Mean ( 13 / 28 ) 9.24457627118644 0.0582254240171869 158.772158850361 Trimmed Mean ( 14 / 28 ) 9.24736842105263 0.0573749737583493 161.174250989647 Trimmed Mean ( 15 / 28 ) 9.24581818181818 0.0573245770322409 161.288903651537 Trimmed Mean ( 16 / 28 ) 9.24415094339623 0.0571819048650528 161.662172066707 Trimmed Mean ( 17 / 28 ) 9.24235294117647 0.0569241588571293 162.362573760173 Trimmed Mean ( 18 / 28 ) 9.24040816326531 0.0565218932837569 163.483698553332 Trimmed Mean ( 19 / 28 ) 9.23829787234042 0.0559364969242194 165.156890050804 Trimmed Mean ( 20 / 28 ) 9.236 0.0551164057411056 167.572610655775 Trimmed Mean ( 21 / 28 ) 9.23348837209302 0.0539911847537241 171.018443366463 Trimmed Mean ( 22 / 28 ) 9.23073170731707 0.0524618214768705 175.951414713779 Trimmed Mean ( 23 / 28 ) 9.22769230769231 0.0503837654840702 183.148127557275 Trimmed Mean ( 24 / 28 ) 9.23243243243243 0.0499450229364943 184.851900942594 Trimmed Mean ( 25 / 28 ) 9.23771428571429 0.0492073057947438 187.730544001883 Trimmed Mean ( 26 / 28 ) 9.24363636363636 0.0480487011890063 192.380566693681 Trimmed Mean ( 27 / 28 ) 9.24258064516129 0.0487057607198363 189.763603084369 Trimmed Mean ( 28 / 28 ) 9.24137931034483 0.0493098281002241 187.414551345857 Median 9.3 Midrange 9.18 Midmean - Weighted Average at Xnp 9.28 Midmean - Weighted Average at X(n+1)p 9.28 Midmean - Empirical Distribution Function 9.28 Midmean - Empirical Distribution Function - Averaging 9.28 Midmean - Empirical Distribution Function - Interpolation 9.28 Midmean - Closest Observation 9.28 Midmean - True Basic - Statistics Graphics Toolkit 9.28 Midmean - MS Excel (old versions) 9.28 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208630145h22lrjhja865326/1n47a1208630064.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208630145h22lrjhja865326/1n47a1208630064.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208630145h22lrjhja865326/256pa1208630064.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208630145h22lrjhja865326/256pa1208630064.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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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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