Duncan Huysmans Opgave 5

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 01 Jun 2009 20:08:58 -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/Jun/02/t1243908567nccf5bz87g2gnwz.htm/, Retrieved Tue, 02 Jun 2009 04:09:29 +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/Jun/02/t1243908567nccf5bz87g2gnwz.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 «

49.1 52.7 55.1 60.4 57.5 55.9 62.6 61.3 67.1 68.6 74.8 76.9 85.7 86.5 90.8 89.7 96.3 107.5 109.2 100.2 116.8 120.1 123.3 130.2 131.4 125.6 124.5 134.3 135.2 151.8 146.4 140.0 127.8 148.0 165.9 165.5 179.9 190.0 189.8 190.9 203.6 183.5 169.3 144.2 141.5 154.3 169.5 194.0 203.2 192.9 209.4 227.2 263.7 297.8 337.1 361.3 355.2 312.6 309.9 323.7 324.1 355.3 383.4 395.1 412.8 407.0 438.0 446.1 452.5 447.3 475.9 487.7

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 197.561111111111 14.8014462553569 13.3474194144786 Geometric Mean 161.837605668408 Harmonic Mean 132.671663985153 Quadratic Mean 233.634912250336 Winsorized Mean ( 1 / 24 ) 197.447222222222 14.7500457509996 13.3862108331997 Winsorized Mean ( 2 / 24 ) 196.863888888889 14.5741304705709 13.5077622151394 Winsorized Mean ( 3 / 24 ) 196.680555555556 14.516463676789 13.5487925940280 Winsorized Mean ( 4 / 24 ) 196.702777777778 14.4881914536326 13.5767654925942 Winsorized Mean ( 5 / 24 ) 196.341666666667 14.3260898213588 13.7051818824939 Winsorized Mean ( 6 / 24 ) 194.316666666667 13.8326756164701 14.0476558588059 Winsorized Mean ( 7 / 24 ) 193.879166666667 13.6910406058020 14.1610248810821 Winsorized Mean ( 8 / 24 ) 193.056944444444 13.3379734922310 14.4742336275368 Winsorized Mean ( 9 / 24 ) 191.781944444444 13.0051810920211 14.7465800812344 Winsorized Mean ( 10 / 24 ) 189.573611111111 12.2695055644468 15.4507946644921 Winsorized Mean ( 11 / 24 ) 188.977777777778 12.0478711004274 15.6855743394428 Winsorized Mean ( 12 / 24 ) 190.427777777778 11.8572705095526 16.0600011296329 Winsorized Mean ( 13 / 24 ) 187.304166666667 11.2114890207415 16.7064487437976 Winsorized Mean ( 14 / 24 ) 185.398611111111 10.6632158614577 17.3867446293793 Winsorized Mean ( 15 / 24 ) 185.544444444444 10.6190644635827 17.4727675004475 Winsorized Mean ( 16 / 24 ) 184.3 10.0180613497891 18.3967729448852 Winsorized Mean ( 17 / 24 ) 184.583333333333 9.79023178978172 18.8538266812015 Winsorized Mean ( 18 / 24 ) 183.383333333333 9.0285722775471 20.3114432377513 Winsorized Mean ( 19 / 24 ) 174.833333333333 7.4065252180727 23.6053112877712 Winsorized Mean ( 20 / 24 ) 166.805555555556 5.48666932244589 30.4019698933114 Winsorized Mean ( 21 / 24 ) 162.576388888889 4.58364680663205 35.4687862628635 Winsorized Mean ( 22 / 24 ) 161.781944444444 4.20503569790006 38.4733819323428 Winsorized Mean ( 23 / 24 ) 162.0375 4.13794061972604 39.1589717908345 Winsorized Mean ( 24 / 24 ) 159.3375 3.67142959831500 43.3993069275053 Trimmed Mean ( 1 / 24 ) 195.537142857143 14.4852556107732 13.499046762538 Trimmed Mean ( 2 / 24 ) 193.514705882353 14.1650823432351 13.6613894076493 Trimmed Mean ( 3 / 24 ) 191.687878787879 13.8902383115034 13.8001864683005 Trimmed Mean ( 4 / 24 ) 189.815625 13.5812778204359 13.9762714164040 Trimmed Mean ( 5 / 24 ) 187.816129032258 13.2129557979189 14.2145430518915 Trimmed Mean ( 6 / 24 ) 185.77 12.8132153486399 14.4983124801472 Trimmed Mean ( 7 / 24 ) 184.001724137931 12.4686550715982 14.7571428579383 Trimmed Mean ( 8 / 24 ) 182.1875 12.0782642767209 15.0839140315170 Trimmed Mean ( 9 / 24 ) 180.375925925926 11.6819318924841 15.4405904422346 Trimmed Mean ( 10 / 24 ) 178.621153846154 11.2676428898707 15.8525749876870 Trimmed Mean ( 11 / 24 ) 177.044 10.9250239471087 16.2053649362348 Trimmed Mean ( 12 / 24 ) 175.416666666667 10.5372403316118 16.6473062344811 Trimmed Mean ( 13 / 24 ) 173.458695652174 10.0708588910168 17.2238234622569 Trimmed Mean ( 14 / 24 ) 171.715909090909 9.63032392675702 17.8307511145925 Trimmed Mean ( 15 / 24 ) 170.040476190476 9.1890899175943 18.5046046687279 Trimmed Mean ( 16 / 24 ) 168.18 8.59993455550531 19.5559627709421 Trimmed Mean ( 17 / 24 ) 166.271052631579 7.96567575005253 20.8734397242422 Trimmed Mean ( 18 / 24 ) 164.116666666667 7.12984727902514 23.0182583502835 Trimmed Mean ( 19 / 24 ) 161.85 6.17628615716493 26.2050682046593 Trimmed Mean ( 20 / 24 ) 160.3125 5.4605711882195 29.358192481009 Trimmed Mean ( 21 / 24 ) 159.533333333333 5.16328847661258 30.8976215557099 Trimmed Mean ( 22 / 24 ) 159.160714285714 5.03272975274575 31.6251263439845 Trimmed Mean ( 23 / 24 ) 158.830769230769 4.94346116440937 32.1294663694897 Trimmed Mean ( 24 / 24 ) 158.4125 4.80284227631508 32.9830735398498 Median 153.05 Midrange 268.4 Midmean - Weighted Average at Xnp 162.389189189189 Midmean - Weighted Average at X(n+1)p 164.116666666667 Midmean - Empirical Distribution Function 162.389189189189 Midmean - Empirical Distribution Function - Averaging 164.116666666667 Midmean - Empirical Distribution Function - Interpolation 164.116666666667 Midmean - Closest Observation 162.389189189189 Midmean - True Basic - Statistics Graphics Toolkit 164.116666666667 Midmean - MS Excel (old versions) 166.271052631579 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243908567nccf5bz87g2gnwz/1beao1243908536.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243908567nccf5bz87g2gnwz/1beao1243908536.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243908567nccf5bz87g2gnwz/2a0tx1243908536.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243908567nccf5bz87g2gnwz/2a0tx1243908536.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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