Centrummaten eigen gegevenreeks citroenen - Lotte Kenis

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 23 Nov 2008 07:41:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227451326bd6zailarvdmzf6.htm/, Retrieved Sun, 23 Nov 2008 14:42:07 +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/Nov/23/t1227451326bd6zailarvdmzf6.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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Dataseries X:

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1.82 1.76 1.79 1.74 1.78 1.80 1.80 1.80 1.79 1.82 1.82 1.83 1.77 1.77 1.77 1.77 1.74 1.78 1.78 1.78 1.78 1.81 1.84 1.80 1.78 1.76 1.74 1.72 1.73 1.77 1.81 1.83 1.87 1.89 1.82 1.79 1.79 1.82 1.82 1.81 1.81 1.78 1.80 1.79 1.83 1.82 1.80 1.82 1.84 1.82 1.81 1.79 1.87 1.89 1.92 1.9 1.91 1.95 2.04 1.99 1.94 1.93 1.89 1.87 1.89 1.9 1.93 1.94 1.88 1.89 1.92 1.91 1.89 1.89 1.98 2.02 2.02 1.99 1.97 1.96 1.95 1.98 2.00 2.00

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 1.85011904761905 0.00869330505125975 212.821134966493 Geometric Mean 1.84845074809645 Harmonic Mean 1.84680964297178 Quadratic Mean 1.85181346124228 Winsorized Mean ( 1 / 28 ) 1.85 0.00861292308464218 214.793512239621 Winsorized Mean ( 2 / 28 ) 1.85023809523810 0.00857449584948022 215.783893037893 Winsorized Mean ( 3 / 28 ) 1.84952380952381 0.00841225638143458 219.860608814255 Winsorized Mean ( 4 / 28 ) 1.84952380952381 0.00841225638143458 219.860608814255 Winsorized Mean ( 5 / 28 ) 1.85011904761905 0.00811296824869498 228.044655285894 Winsorized Mean ( 6 / 28 ) 1.85011904761905 0.00811296824869498 228.044655285894 Winsorized Mean ( 7 / 28 ) 1.85011904761905 0.0078359800358093 236.105635691294 Winsorized Mean ( 8 / 28 ) 1.85011904761905 0.0078359800358093 236.105635691294 Winsorized Mean ( 9 / 28 ) 1.84904761904762 0.00762657402208705 242.448000070891 Winsorized Mean ( 10 / 28 ) 1.84785714285714 0.00740414249733281 249.570715788195 Winsorized Mean ( 11 / 28 ) 1.84654761904762 0.00717075971048819 257.510737160359 Winsorized Mean ( 12 / 28 ) 1.84797619047619 0.0069951621711762 264.179177730981 Winsorized Mean ( 13 / 28 ) 1.84642857142857 0.006729429583757 274.381141588188 Winsorized Mean ( 14 / 28 ) 1.84642857142857 0.006729429583757 274.381141588188 Winsorized Mean ( 15 / 28 ) 1.84464285714286 0.00643705216083175 286.566398881644 Winsorized Mean ( 16 / 28 ) 1.84464285714286 0.00643705216083175 286.566398881644 Winsorized Mean ( 17 / 28 ) 1.84261904761905 0.00612107484875377 301.028674399268 Winsorized Mean ( 18 / 28 ) 1.84261904761905 0.00612107484875377 301.028674399268 Winsorized Mean ( 19 / 28 ) 1.84261904761905 0.00551199351484723 334.292673359598 Winsorized Mean ( 20 / 28 ) 1.84261904761905 0.00551199351484723 334.292673359598 Winsorized Mean ( 21 / 28 ) 1.84011904761905 0.00515256078132523 357.127091889593 Winsorized Mean ( 22 / 28 ) 1.84011904761905 0.00515256078132523 357.127091889593 Winsorized Mean ( 23 / 28 ) 1.83738095238095 0.00477887109463709 384.480124279327 Winsorized Mean ( 24 / 28 ) 1.83738095238095 0.00477887109463709 384.480124279327 Winsorized Mean ( 25 / 28 ) 1.84035714285714 0.00443751295060509 414.727159862417 Winsorized Mean ( 26 / 28 ) 1.84035714285714 0.00443751295060509 414.727159862417 Winsorized Mean ( 27 / 28 ) 1.84035714285714 0.00443751295060509 414.727159862417 Winsorized Mean ( 28 / 28 ) 1.84035714285714 0.00443751295060509 414.727159862417 Trimmed Mean ( 1 / 28 ) 1.84939024390244 0.0084465614964545 218.951847409000 Trimmed Mean ( 2 / 28 ) 1.84875 0.00825306809080068 224.007602949589 Trimmed Mean ( 3 / 28 ) 1.84794871794872 0.00805070299166305 229.538801749657 Trimmed Mean ( 4 / 28 ) 1.84736842105263 0.00788596003356405 234.260434137366 Trimmed Mean ( 5 / 28 ) 1.84675675675676 0.00769202674095011 240.087147243673 Trimmed Mean ( 6 / 28 ) 1.84597222222222 0.00755175083136505 244.442946204641 Trimmed Mean ( 7 / 28 ) 1.84514285714286 0.0073840039107064 249.883786554812 Trimmed Mean ( 8 / 28 ) 1.84426470588235 0.00724982569640184 254.387454693936 Trimmed Mean ( 9 / 28 ) 1.84333333333333 0.00708698315401766 260.101272046672 Trimmed Mean ( 10 / 28 ) 1.8425 0.0069365033961701 265.623743659855 Trimmed Mean ( 11 / 28 ) 1.84177419354839 0.00680048911649786 270.829665631003 Trimmed Mean ( 12 / 28 ) 1.84116666666667 0.00668116361641467 275.575748832611 Trimmed Mean ( 13 / 28 ) 1.84034482758621 0.00656285868891615 280.418170620422 Trimmed Mean ( 14 / 28 ) 1.83964285714286 0.00646651859262152 284.487368402828 Trimmed Mean ( 15 / 28 ) 1.83888888888889 0.00634257665251737 289.927735939783 Trimmed Mean ( 16 / 28 ) 1.83826923076923 0.00624246848681757 294.477935235262 Trimmed Mean ( 17 / 28 ) 1.8376 0.00611161490399172 300.673394653808 Trimmed Mean ( 18 / 28 ) 1.83708333333333 0.0060064853641926 305.849964154583 Trimmed Mean ( 19 / 28 ) 1.83652173913043 0.00586661224698366 313.046382104883 Trimmed Mean ( 20 / 28 ) 1.83590909090909 0.00580076343501295 316.494391036133 Trimmed Mean ( 21 / 28 ) 1.83523809523810 0.00570508357002856 321.68469974383 Trimmed Mean ( 22 / 28 ) 1.83475 0.0056499092345784 324.739730113011 Trimmed Mean ( 23 / 28 ) 1.83421052631579 0.0055639509656477 329.659721597181 Trimmed Mean ( 24 / 28 ) 1.83388888888889 0.00552451646634787 331.954642557384 Trimmed Mean ( 25 / 28 ) 1.83352941176471 0.00545410854214641 336.17398656374 Trimmed Mean ( 26 / 28 ) 1.8328125 0.00541120356223414 338.706995388524 Trimmed Mean ( 27 / 28 ) 1.832 0.00532614458045911 343.963625531563 Trimmed Mean ( 28 / 28 ) 1.83107142857143 0.00517777315503963 353.640720391392 Median 1.82 Midrange 1.88 Midmean - Weighted Average at Xnp 1.83318181818182 Midmean - Weighted Average at X(n+1)p 1.83318181818182 Midmean - Empirical Distribution Function 1.83318181818182 Midmean - Empirical Distribution Function - Averaging 1.83318181818182 Midmean - Empirical Distribution Function - Interpolation 1.83318181818182 Midmean - Closest Observation 1.83318181818182 Midmean - True Basic - Statistics Graphics Toolkit 1.83318181818182 Midmean - MS Excel (old versions) 1.83652173913043 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227451326bd6zailarvdmzf6/1jhrh1227451287.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227451326bd6zailarvdmzf6/1jhrh1227451287.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227451326bd6zailarvdmzf6/2nj1z1227451287.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227451326bd6zailarvdmzf6/2nj1z1227451287.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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