Investeringsgoederen

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Fri, 05 Dec 2008 08:25:20 -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/Dec/05/t1228490830qrtbmfud0qd4yn0.htm/, Retrieved Fri, 05 Dec 2008 15:27:12 +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/Dec/05/t1228490830qrtbmfud0qd4yn0.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

119,5 125 145 105,3 116,9 120,1 88,9 78,4 114,6 113,3 117 99,6 99,4 101,9 115,2 108,5 113,8 121 92,2 90,2 101,5 126,6 93,9 89,8 93,4 101,5 110,4 105,9 108,4 113,9 86,1 69,4 101,2 100,5 98 106,6 90,1 96,9 125,9 112 100 123,9 79,8 83,4 113,6 112,9 104 109,9 99 106,3 128,9 111,1 102,9 130 87 87,5 117,6 103,4 110,8 112,6 102,5 112,4 135,6 105,1 127,7 137 91 90,5 122,4 123,3 124,3 120 118,1 119 142,7 123,6 129,6 151,6 110,4 99,2 130,5 136,2 129,7 128 121,6

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 110.287058823529 1.75366106700069 62.8896090007603 Geometric Mean 109.089326026462 Harmonic Mean 107.859567066814 Quadratic Mean 111.452065138020 Winsorized Mean ( 1 / 28 ) 110.315294117647 1.70684197871001 64.6312286044316 Winsorized Mean ( 2 / 28 ) 110.294117647059 1.68689407874011 65.3829538185552 Winsorized Mean ( 3 / 28 ) 110.22 1.61776707474322 68.130945252112 Winsorized Mean ( 4 / 28 ) 110.309411764706 1.58630926893877 69.5384020787462 Winsorized Mean ( 5 / 28 ) 110.327058823529 1.57000632323594 70.2717289673933 Winsorized Mean ( 6 / 28 ) 110.002352941176 1.49983470281627 73.3429842199431 Winsorized Mean ( 7 / 28 ) 110.076470588235 1.47300322714092 74.7292799907113 Winsorized Mean ( 8 / 28 ) 110.132941176471 1.45416853545613 75.7360226763022 Winsorized Mean ( 9 / 28 ) 110.154117647059 1.44720976872089 76.114824559551 Winsorized Mean ( 10 / 28 ) 110.083529411765 1.43223967825329 76.8611085722878 Winsorized Mean ( 11 / 28 ) 110.005882352941 1.40785844970333 78.1370331485543 Winsorized Mean ( 12 / 28 ) 110.034117647059 1.38985575792829 79.1694512321729 Winsorized Mean ( 13 / 28 ) 110.049411764706 1.33513459232926 82.4257062898171 Winsorized Mean ( 14 / 28 ) 110.131764705882 1.28718986013548 85.5598448346159 Winsorized Mean ( 15 / 28 ) 110.061176470588 1.25069850972739 87.9997662222994 Winsorized Mean ( 16 / 28 ) 110.494117647059 1.14853012011441 96.2048062231508 Winsorized Mean ( 17 / 28 ) 110.634117647059 1.10663716120412 99.9732536784495 Winsorized Mean ( 18 / 28 ) 110.782352941176 1.06928230134686 103.604401570695 Winsorized Mean ( 19 / 28 ) 110.76 1.05389659797140 105.095699343937 Winsorized Mean ( 20 / 28 ) 110.595294117647 1.01812414133909 108.626531507431 Winsorized Mean ( 21 / 28 ) 110.447058823529 0.984678975165245 112.165550000694 Winsorized Mean ( 22 / 28 ) 110.395294117647 0.950361726625795 116.161342596991 Winsorized Mean ( 23 / 28 ) 110.287058823529 0.90082562229298 122.428865358872 Winsorized Mean ( 24 / 28 ) 110.456470588235 0.87187850106133 126.687916325242 Winsorized Mean ( 25 / 28 ) 110.397647058824 0.841700254155115 131.160287185180 Winsorized Mean ( 26 / 28 ) 110.244705882353 0.822158983791115 134.091712254965 Winsorized Mean ( 27 / 28 ) 110.085882352941 0.770236154519369 142.924844162418 Winsorized Mean ( 28 / 28 ) 110.118823529412 0.725047074908757 151.878170866726 Trimmed Mean ( 1 / 28 ) 110.281927710843 1.65222416152425 66.7475577945206 Trimmed Mean ( 2 / 28 ) 110.246913580247 1.58880252914079 69.3899408882911 Trimmed Mean ( 3 / 28 ) 110.221518987342 1.52748026034762 72.1590464038193 Trimmed Mean ( 4 / 28 ) 110.222077922078 1.48705237137683 74.1211809642091 Trimmed Mean ( 5 / 28 ) 110.197333333333 1.45093318630153 75.9492817269067 Trimmed Mean ( 6 / 28 ) 110.167123287671 1.41343447395191 77.9428585604313 Trimmed Mean ( 7 / 28 ) 110.2 1.38786926132079 79.4022917512607 Trimmed Mean ( 8 / 28 ) 110.221739130435 1.36383671856537 80.8174011082339 Trimmed Mean ( 9 / 28 ) 110.235820895522 1.33921931512547 82.3134938769862 Trimmed Mean ( 10 / 28 ) 110.247692307692 1.31105342937447 84.0909224884098 Trimmed Mean ( 11 / 28 ) 110.269841269841 1.28010223230180 86.1414334631388 Trimmed Mean ( 12 / 28 ) 110.303278688525 1.24743883456196 88.4237973297165 Trimmed Mean ( 13 / 28 ) 110.335593220339 1.21119066744903 91.0967993608505 Trimmed Mean ( 14 / 28 ) 110.368421052632 1.17760578093023 93.7227235462852 Trimmed Mean ( 15 / 28 ) 110.394545454545 1.14552685357792 96.3701070033764 Trimmed Mean ( 16 / 28 ) 110.430188679245 1.11264530339126 99.2501279092824 Trimmed Mean ( 17 / 28 ) 110.423529411765 1.09121838088745 101.192878846085 Trimmed Mean ( 18 / 28 ) 110.402040816327 1.07151781293391 103.033322902991 Trimmed Mean ( 19 / 28 ) 110.363829787234 1.05276792798483 104.832059235019 Trimmed Mean ( 20 / 28 ) 110.324444444444 1.03087270842001 107.020433796851 Trimmed Mean ( 21 / 28 ) 110.297674418605 1.00908107255395 109.305067173091 Trimmed Mean ( 22 / 28 ) 110.282926829268 0.986728410746071 111.766242492078 Trimmed Mean ( 23 / 28 ) 110.271794871795 0.963629754566528 114.433779518772 Trimmed Mean ( 24 / 28 ) 110.270270270270 0.942839816667108 116.955466157624 Trimmed Mean ( 25 / 28 ) 110.251428571429 0.919959548147684 119.843778776379 Trimmed Mean ( 26 / 28 ) 110.236363636364 0.89453113440127 123.233680077717 Trimmed Mean ( 27 / 28 ) 110.235483870968 0.86252378352244 127.805732406334 Trimmed Mean ( 28 / 28 ) 110.251724137931 0.830849477598081 132.697590972386 Median 110.8 Midrange 110.5 Midmean - Weighted Average at Xnp 110.028571428571 Midmean - Weighted Average at X(n+1)p 110.297674418605 Midmean - Empirical Distribution Function 110.297674418605 Midmean - Empirical Distribution Function - Averaging 110.297674418605 Midmean - Empirical Distribution Function - Interpolation 110.297674418605 Midmean - Closest Observation 110.05 Midmean - True Basic - Statistics Graphics Toolkit 110.297674418605 Midmean - MS Excel (old versions) 110.297674418605 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490830qrtbmfud0qd4yn0/1xvm21228490718.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490830qrtbmfud0qd4yn0/1xvm21228490718.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490830qrtbmfud0qd4yn0/2jevp1228490718.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490830qrtbmfud0qd4yn0/2jevp1228490718.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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