Vincent Van Roy, Central Tendency, eigen gegevens

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 29 May 2009 04:20:56 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/May/29/t1243592535xeotojsp17xqdsz.htm/, Retrieved Fri, 29 May 2009 12:22:18 +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/May/29/t1243592535xeotojsp17xqdsz.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

4.73 4.73 4.73 4.73 4.74 4.74 4.74 4.74 4.74 4.76 4.76 4.76 4.76 4.76 4.76 4.77 4.77 4.78 4.78 4.79 4.83 4.84 4.85 4.85 4.86 4.87 4.87 4.9 4.9 4.92 4.92 4.95 4.96 4.95 4.95 4.95 4.96 4.96 4.96 4.96 4.97 4.97 4.97 5.03 5.08 5.1 5.11 5.13 5.13 5.13 5.15 5.15 5.15 5.17 5.17 5.18 5.2 5.22 5.23 5.23 5.26 5.27 5.28 5.31 5.31 5.32 5.33 5.34 5.38 5.39 5.41 5.44 5.44 5.44 5.46 5.47 5.47 5.49 5.49 5.5 5.52 5.59 5.6 5.6

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 5.06976190476191 0.0292304120340204 173.441342491558 Geometric Mean 5.06284479712875 Harmonic Mean 5.05601101490532 Quadratic Mean 5.07675116397804 Winsorized Mean ( 1 / 28 ) 5.06976190476191 0.0292304120340204 173.441342491558 Winsorized Mean ( 2 / 28 ) 5.06952380952381 0.0291788089282866 173.739915908949 Winsorized Mean ( 3 / 28 ) 5.06702380952381 0.0286719729984788 176.723932105846 Winsorized Mean ( 4 / 28 ) 5.06654761904762 0.0284271643537688 178.229089472158 Winsorized Mean ( 5 / 28 ) 5.06595238095238 0.0283187936678562 178.890119415736 Winsorized Mean ( 6 / 28 ) 5.06595238095238 0.0283187936678562 178.890119415736 Winsorized Mean ( 7 / 28 ) 5.06428571428571 0.0280230653063654 180.718478115075 Winsorized Mean ( 8 / 28 ) 5.06428571428571 0.0280230653063654 180.718478115075 Winsorized Mean ( 9 / 28 ) 5.06535714285714 0.0275445950564987 183.896591417199 Winsorized Mean ( 10 / 28 ) 5.06297619047619 0.0271397964827311 186.551737545185 Winsorized Mean ( 11 / 28 ) 5.06297619047619 0.0271397964827311 186.551737545185 Winsorized Mean ( 12 / 28 ) 5.06297619047619 0.0271397964827311 186.551737545185 Winsorized Mean ( 13 / 28 ) 5.05833333333333 0.0263781545539962 191.762214562012 Winsorized Mean ( 14 / 28 ) 5.055 0.0258501462879725 195.550150613731 Winsorized Mean ( 15 / 28 ) 5.055 0.0253288752607298 199.574594132782 Winsorized Mean ( 16 / 28 ) 5.04738095238095 0.0241838192917698 208.709008758541 Winsorized Mean ( 17 / 28 ) 5.04738095238095 0.0236124517699706 213.759291138077 Winsorized Mean ( 18 / 28 ) 5.04523809523810 0.0233057431692769 216.480464003785 Winsorized Mean ( 19 / 28 ) 5.04523809523810 0.0226775370839727 222.477338546778 Winsorized Mean ( 20 / 28 ) 5.05476190476190 0.0214287945420908 235.886432847786 Winsorized Mean ( 21 / 28 ) 5.04976190476190 0.0200558430017415 251.785073523133 Winsorized Mean ( 22 / 28 ) 5.04976190476190 0.0193674912831347 260.733919067734 Winsorized Mean ( 23 / 28 ) 5.04702380952381 0.0189949564235497 265.703363407908 Winsorized Mean ( 24 / 28 ) 5.04130952380952 0.0175015610826585 288.049134588612 Winsorized Mean ( 25 / 28 ) 5.04428571428571 0.0171334120088497 294.412211162625 Winsorized Mean ( 26 / 28 ) 5.04119047619048 0.0167320045409465 301.290288551721 Winsorized Mean ( 27 / 28 ) 5.04440476190476 0.0147442834790005 342.126137841099 Winsorized Mean ( 28 / 28 ) 5.03773809523809 0.0139093359585045 362.183939640764 Trimmed Mean ( 1 / 28 ) 5.06743902439024 0.0289325347674578 175.146735850117 Trimmed Mean ( 2 / 28 ) 5.065 0.0285792258799768 177.226633823859 Trimmed Mean ( 3 / 28 ) 5.0625641025641 0.0281925470684067 179.571008262583 Trimmed Mean ( 4 / 28 ) 5.06092105263158 0.0279524518785082 181.054637876786 Trimmed Mean ( 5 / 28 ) 5.05932432432432 0.0277426230099612 182.366473512895 Trimmed Mean ( 6 / 28 ) 5.05777777777778 0.0275145588309403 183.821874406733 Trimmed Mean ( 7 / 28 ) 5.05614285714286 0.0272328300663384 185.663511461212 Trimmed Mean ( 8 / 28 ) 5.05470588235294 0.0269567586852778 187.511634516858 Trimmed Mean ( 9 / 28 ) 5.05318181818182 0.0266157664781086 189.856708516663 Trimmed Mean ( 10 / 28 ) 5.05140625 0.0262928289942870 192.121062784746 Trimmed Mean ( 11 / 28 ) 5.04983870967742 0.0259728654073072 194.427477695884 Trimmed Mean ( 12 / 28 ) 5.04816666666667 0.025571978469851 197.410093732809 Trimmed Mean ( 13 / 28 ) 5.04637931034483 0.0250718245631327 201.276907376153 Trimmed Mean ( 14 / 28 ) 5.045 0.0245993875966429 205.086406325355 Trimmed Mean ( 15 / 28 ) 5.04388888888889 0.0241087343890370 209.214171407625 Trimmed Mean ( 16 / 28 ) 5.04269230769231 0.0235869358614995 213.791750539475 Trimmed Mean ( 17 / 28 ) 5.0422 0.0231468955912063 217.834827142677 Trimmed Mean ( 18 / 28 ) 5.04166666666667 0.0226860576214090 222.23635110178 Trimmed Mean ( 19 / 28 ) 5.04130434782609 0.0221449085666509 227.650718568241 Trimmed Mean ( 20 / 28 ) 5.04090909090909 0.0215636581113588 233.768735567819 Trimmed Mean ( 21 / 28 ) 5.03952380952381 0.0210467991915202 239.443716057036 Trimmed Mean ( 22 / 28 ) 5.0385 0.0206483065674298 244.015168195324 Trimmed Mean ( 23 / 28 ) 5.03736842105263 0.0202392665494315 248.890858211170 Trimmed Mean ( 24 / 28 ) 5.03638888888889 0.0197450125419607 255.071445418731 Trimmed Mean ( 25 / 28 ) 5.03588235294118 0.0194079832107808 259.474789227137 Trimmed Mean ( 26 / 28 ) 5.035 0.0189811026567087 265.263830614204 Trimmed Mean ( 27 / 28 ) 5.03433333333333 0.0184433480724787 272.962008500267 Trimmed Mean ( 28 / 28 ) 5.03321428571429 0.0181997555904614 276.553949348211 Median 4.97 Midrange 5.165 Midmean - Weighted Average at Xnp 5.0346511627907 Midmean - Weighted Average at X(n+1)p 5.03952380952381 Midmean - Empirical Distribution Function 5.0346511627907 Midmean - Empirical Distribution Function - Averaging 5.03952380952381 Midmean - Empirical Distribution Function - Interpolation 5.03952380952381 Midmean - Closest Observation 5.0346511627907 Midmean - True Basic - Statistics Graphics Toolkit 5.03952380952381 Midmean - MS Excel (old versions) 5.04688888888889 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243592535xeotojsp17xqdsz/1unio1243592454.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243592535xeotojsp17xqdsz/1unio1243592454.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243592535xeotojsp17xqdsz/2nvtp1243592454.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/29/t1243592535xeotojsp17xqdsz/2nvtp1243592454.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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