gemiddelde Q9 van GI / NIC

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 26 Oct 2008 05:54:18 -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/Oct/26/t1225022163wanmdu2315rk0iu.htm/, Retrieved Sun, 26 Oct 2008 11:56:05 +0000

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/2008/Oct/26/t1225022163wanmdu2315rk0iu.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

gem Q9 GI / NIC

Dataseries X:

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0,66666667 0,63157895 0,63636364 0,71428571 0,63636364 0,66666667 0,71428571 0,79310345 0,76470588 0,76666667 0,80645161 0,92000000 0,95454545 0,95652174 1,04761905 0,96428571 1,00000000 1,10344828 1,19230769 1,14814815 1,21739130 1,30434783 1,33333333 1,22727273 1,10344828 1,19230769 1,11111111 1,11111111 1,30769231 1,33333333 1,07692308 1,00000000 1,00000000 0,84615385 0,81818182 0,85714286 0,75000000 0,76470588 0,77777778 1,00000000 1,10000000 1,00000000 1,00000000 0,88888889 0,94444444 1,00000000 0,89473684 0,94117647 1,00000000 1,00000000 1,00000000 0,84210526 0,73076923 0,69565217 0,70833333 0,72727273 0,70000000 0,72413793 0,73076923 0,73913043 0,78260870 0,76923077 0,80645161 0,75000000 0,84000000 0,79310345 0,77419355 0,77419355 0,71875000 0,68000000 0,76923077 0,79310345

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.900479607777778 0.0222106384298357 40.5427160782626 Geometric Mean 0.882054964037387 Harmonic Mean 0.864782595021076 Quadratic Mean 0.919722082286461 Winsorized Mean ( 1 / 24 ) 0.900546061805556 0.0221994033367176 40.5662282065059 Winsorized Mean ( 2 / 24 ) 0.89983381125 0.0220086438490936 40.8854728814678 Winsorized Mean ( 3 / 24 ) 0.900957084166667 0.0217700766403039 41.3851131097391 Winsorized Mean ( 4 / 24 ) 0.896675134166667 0.0207284833094616 43.2581159354469 Winsorized Mean ( 5 / 24 ) 0.896914849444445 0.0204340160578352 43.8932242641815 Winsorized Mean ( 6 / 24 ) 0.896128896111111 0.0197920745414456 45.2771585027417 Winsorized Mean ( 7 / 24 ) 0.896551601805556 0.0197322696685639 45.4358072773494 Winsorized Mean ( 8 / 24 ) 0.892570911805556 0.0186090134125712 47.964440242844 Winsorized Mean ( 9 / 24 ) 0.888685329305556 0.0176456321707983 50.362906848769 Winsorized Mean ( 10 / 24 ) 0.888685329305555 0.0176456321707983 50.362906848769 Winsorized Mean ( 11 / 24 ) 0.888196663472222 0.0173449834443257 51.2076973911894 Winsorized Mean ( 12 / 24 ) 0.889094651805556 0.0172226307309629 51.6236262446908 Winsorized Mean ( 13 / 24 ) 0.88903805125 0.0170377456234987 52.1804979893483 Winsorized Mean ( 14 / 24 ) 0.885230747361111 0.0161805145282118 54.7096784726872 Winsorized Mean ( 15 / 24 ) 0.879125741111111 0.0151933579750168 57.8625042967265 Winsorized Mean ( 16 / 24 ) 0.870401774444444 0.0133825291154840 65.0401554843143 Winsorized Mean ( 17 / 24 ) 0.872968200694444 0.0130346510188289 66.972886303854 Winsorized Mean ( 18 / 24 ) 0.872968200694444 0.0130346510188289 66.972886303854 Winsorized Mean ( 19 / 24 ) 0.876848919027778 0.0125320156374827 69.9687061038416 Winsorized Mean ( 20 / 24 ) 0.876848919027778 0.0125320156374827 69.9687061038416 Winsorized Mean ( 21 / 24 ) 0.877420816111111 0.0124601767228791 70.4180073545837 Winsorized Mean ( 22 / 24 ) 0.878204291111111 0.0123624973247778 71.0377740063044 Winsorized Mean ( 23 / 24 ) 0.878204291111111 0.0123624973247778 71.0377740063044 Winsorized Mean ( 24 / 24 ) 0.879858551111111 0.0121585518652705 72.3654067409398 Trimmed Mean ( 1 / 24 ) 0.898137421142857 0.0216396202052605 41.5043061118293 Trimmed Mean ( 2 / 24 ) 0.895587095735294 0.0209696679908977 42.7086921988484 Trimmed Mean ( 3 / 24 ) 0.893270705454545 0.0202893662343817 44.0265454886825 Trimmed Mean ( 4 / 24 ) 0.8903883134375 0.0195760431253164 45.4835692656407 Trimmed Mean ( 5 / 24 ) 0.888563107419355 0.0191116837480304 46.4931881007569 Trimmed Mean ( 6 / 24 ) 0.886558689333333 0.0186366710967749 47.5706570518783 Trimmed Mean ( 7 / 24 ) 0.884578646551724 0.0182356786519553 48.5081286764655 Trimmed Mean ( 8 / 24 ) 0.882379532321429 0.0177495189031381 49.7128703677386 Trimmed Mean ( 9 / 24 ) 0.880680969074074 0.0174276889036289 50.5334341199246 Trimmed Mean ( 10 / 24 ) 0.879449529038462 0.0172418994835339 51.0065338148119 Trimmed Mean ( 11 / 24 ) 0.8781195738 0.0169917166026487 51.6792737505473 Trimmed Mean ( 12 / 24 ) 0.876745425208333 0.0167254879998393 52.4197216378235 Trimmed Mean ( 13 / 24 ) 0.875134656521739 0.0163933422051657 53.3835410479002 Trimmed Mean ( 14 / 24 ) 0.873384578863636 0.0159897714422212 54.621454848157 Trimmed Mean ( 15 / 24 ) 0.871934027619048 0.0156522437529979 55.7066476460952 Trimmed Mean ( 16 / 24 ) 0.871071022 0.0154225727527754 56.4802666820454 Trimmed Mean ( 17 / 24 ) 0.871150275 0.0154823749337395 56.267225069041 Trimmed Mean ( 18 / 24 ) 0.870936401388889 0.0155773146806514 55.9105609178378 Trimmed Mean ( 19 / 24 ) 0.87069736617647 0.0156401568140331 55.6706289156408 Trimmed Mean ( 20 / 24 ) 0.8699688928125 0.0157630874641827 55.1902598262725 Trimmed Mean ( 21 / 24 ) 0.869143289666667 0.0158469072247386 54.8462408052624 Trimmed Mean ( 22 / 24 ) 0.868129715 0.0158875257260598 54.6422224560768 Trimmed Mean ( 23 / 24 ) 0.866861586538462 0.0158653953783103 54.6385114186031 Trimmed Mean ( 24 / 24 ) 0.865382103333333 0.0157138044211552 55.0714569266424 Median 0.844129555 Midrange 0.98245614 Midmean - Weighted Average at Xnp 0.874454114102564 Midmean - Weighted Average at X(n+1)p 0.874454114102564 Midmean - Empirical Distribution Function 0.874454114102564 Midmean - Empirical Distribution Function - Averaging 0.874454114102564 Midmean - Empirical Distribution Function - Interpolation 0.874454114102564 Midmean - Closest Observation 0.874454114102564 Midmean - True Basic - Statistics Graphics Toolkit 0.874454114102564 Midmean - MS Excel (old versions) 0.874454114102564 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225022163wanmdu2315rk0iu/1tt1n1225022056.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225022163wanmdu2315rk0iu/1tt1n1225022056.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225022163wanmdu2315rk0iu/2pxop1225022056.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225022163wanmdu2315rk0iu/2pxop1225022056.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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