Centrummaten Sales '66 - '71; 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: Sun, 14 Mar 2010 12:51:55 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/14/t12685928705r0hst2yqyc2q6s.htm/, Retrieved Sun, 14 Mar 2010 19:54:32 +0100

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/2010/Mar/14/t12685928705r0hst2yqyc2q6s.htm/}, year = {2010}, } @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 = {2010}, 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 «

164 96 73 49 39 59 169 169 210 278 298 245 200 188 90 79 78 91 167 169 289 247 275 203 223 104 107 85 75 99 135 211 335 488 326 346 261 224 141 148 145 223 272 445 560 612 467 404 518 404 300 210 196 186 247 343 464 680 711 610 513 292 273 322 189 257 324 404 677 858 895 664 628 308 324 248 272

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 R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 294.519480519481 22.1083565510444 13.3216360899321 Geometric Mean 236.358840652421 Harmonic Mean 183.164793041416 Quadratic Mean 351.978637191181 Winsorized Mean ( 1 / 25 ) 294.168831168831 21.9217321065201 13.4190505448854 Winsorized Mean ( 2 / 25 ) 290.610389610390 20.7240532406636 14.0228548071943 Winsorized Mean ( 3 / 25 ) 289.948051948052 20.3319336094902 14.2607219518322 Winsorized Mean ( 4 / 25 ) 289.896103896104 20.2781544775212 14.2959806434782 Winsorized Mean ( 5 / 25 ) 289.246753246753 20.0411841503364 14.4326179070561 Winsorized Mean ( 6 / 25 ) 286.519480519481 19.3593178801994 14.8000814022756 Winsorized Mean ( 7 / 25 ) 285.610389610390 18.9491905789343 15.0724321664642 Winsorized Mean ( 8 / 25 ) 285.922077922078 18.8303735660674 15.1840895199930 Winsorized Mean ( 9 / 25 ) 280.194805194805 17.5372179078783 15.9771525145350 Winsorized Mean ( 10 / 25 ) 275.389610389610 16.3374065563795 16.8563847290728 Winsorized Mean ( 11 / 25 ) 275.103896103896 16.1366090578233 17.0484328595989 Winsorized Mean ( 12 / 25 ) 271.987012987013 15.2837425577283 17.7958384184823 Winsorized Mean ( 13 / 25 ) 268.948051948052 14.5628824346874 18.4680507553535 Winsorized Mean ( 14 / 25 ) 273.493506493507 13.7536749998033 19.885122085364 Winsorized Mean ( 15 / 25 ) 270.961038961039 12.9337187423137 20.9499714938572 Winsorized Mean ( 16 / 25 ) 263.272727272727 11.370201794431 23.1546222338530 Winsorized Mean ( 17 / 25 ) 263.935064935065 11.2800875502330 23.3983170573541 Winsorized Mean ( 18 / 25 ) 267.675324675325 10.7903883959580 24.8068294534785 Winsorized Mean ( 19 / 25 ) 254.103896103896 8.46153664113782 30.0304669093446 Winsorized Mean ( 20 / 25 ) 253.844155844156 8.28045787066567 30.6558115274547 Winsorized Mean ( 21 / 25 ) 251.662337662338 7.97583950780578 31.5530844641547 Winsorized Mean ( 22 / 25 ) 249.090909090909 7.6283768408244 32.6531992701071 Winsorized Mean ( 23 / 25 ) 253.571428571429 6.86789286087105 36.9212848406707 Winsorized Mean ( 24 / 25 ) 254.194805194805 6.7875443541748 37.4501869793982 Winsorized Mean ( 25 / 25 ) 253.87012987013 6.6582515693549 38.1286479229151 Trimmed Mean ( 1 / 25 ) 289.92 20.9369861964656 13.8472651832259 Trimmed Mean ( 2 / 25 ) 285.438356164384 19.7523671230562 14.4508429995310 Trimmed Mean ( 3 / 25 ) 282.633802816901 19.1243125828156 14.7787692547373 Trimmed Mean ( 4 / 25 ) 279.913043478261 18.5548165910007 15.0857348605656 Trimmed Mean ( 5 / 25 ) 279.913043478261 17.8892319316003 15.6470129376438 Trimmed Mean ( 6 / 25 ) 274.153846153846 17.1619300113937 15.9745346806470 Trimmed Mean ( 7 / 25 ) 271.634920634921 16.4856576494485 16.4770448599003 Trimmed Mean ( 8 / 25 ) 269.114754098361 15.7723923283667 17.0623928504718 Trimmed Mean ( 9 / 25 ) 266.372881355932 14.9200459865722 17.8533552507589 Trimmed Mean ( 10 / 25 ) 266.372881355932 14.2100463268669 18.7453914806950 Trimmed Mean ( 11 / 25 ) 262.745454545455 13.6295929319052 19.2775716676321 Trimmed Mean ( 12 / 25 ) 261.11320754717 12.9493727923987 20.1641586610622 Trimmed Mean ( 13 / 25 ) 259.745098039216 12.3015332421471 21.1148555977791 Trimmed Mean ( 14 / 25 ) 258.632653061225 11.6558390186726 22.1891064767536 Trimmed Mean ( 15 / 25 ) 256.893617021277 11.0070297125107 23.3390500190336 Trimmed Mean ( 16 / 25 ) 255.288888888889 10.37200107429 24.6132725074331 Trimmed Mean ( 17 / 25 ) 254.395348837209 9.94704358683348 25.5749707555260 Trimmed Mean ( 18 / 25 ) 253.341463414634 9.40112926248092 26.9479821350503 Trimmed Mean ( 19 / 25 ) 251.769230769231 8.77707582887866 28.6848644899307 Trimmed Mean ( 20 / 25 ) 251.769230769231 8.58193346597647 29.3371221959927 Trimmed Mean ( 21 / 25 ) 251.257142857143 8.34752948478769 30.0995813569784 Trimmed Mean ( 22 / 25 ) 251.212121212121 8.09165741063325 31.0458177433468 Trimmed Mean ( 23 / 25 ) 251.451612903226 7.81421900963168 32.1787260624882 Trimmed Mean ( 24 / 25 ) 251.206896551724 7.6273069368699 32.9352022451603 Trimmed Mean ( 25 / 25 ) 250.851851851852 7.35170652974129 34.1215812732774 Median 248 Midrange 467 Midmean - Weighted Average at Xnp 249.289473684211 Midmean - Weighted Average at X(n+1)p 251.769230769231 Midmean - Empirical Distribution Function 251.769230769231 Midmean - Empirical Distribution Function - Averaging 251.769230769231 Midmean - Empirical Distribution Function - Interpolation 251.769230769231 Midmean - Closest Observation 249.575 Midmean - True Basic - Statistics Graphics Toolkit 251.769230769231 Midmean - MS Excel (old versions) 251.769230769231 Number of observations 77

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/14/t12685928705r0hst2yqyc2q6s/1kox01268592713.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t12685928705r0hst2yqyc2q6s/1kox01268592713.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t12685928705r0hst2yqyc2q6s/27ry01268592714.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t12685928705r0hst2yqyc2q6s/27ry01268592714.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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