Central Tendency Niet-duurzame consumptiegoederen

*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, 12 Dec 2008 03:34:15 -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/12/t122907811973hw8vx6lbe9cuf.htm/, Retrieved Fri, 12 Dec 2008 11:35:26 +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/2008/Dec/12/t122907811973hw8vx6lbe9cuf.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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99,5 98,2 108,9 100,0 105,0 108,4 96,7 100,5 115,6 114,9 110,7 107,7 113,5 106,9 119,6 109,4 106,9 118,7 108,9 113,1 125,1 126,5 122,7 127,5 107,1 112,0 122,1 111,5 113,2 128,2 115,1 117,4 132,0 130,8 128,0 132,7 117,0 110,9 123,5 117,4 122,7 123,5 111,5 113,8 131,2 127,0 126,2 121,2 118,8 117,9 135,2 120,7 126,4 129,6 113,4 120,5 135,5 137,6 130,6 133,1 121,5 120,5 136,9 123,7 128,5 135,0 120,9 121,1 132,2 134,5 133,6 136,1 124,5 124,6 133,5 132,3 125,3 135,5 121,2 117,5 135,9

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 120.679012345679 1.15860537179828 104.158857953828 Geometric Mean 120.222901828771 Harmonic Mean 119.755693811144 Quadratic Mean 121.123132940547 Winsorized Mean ( 1 / 27 ) 120.688888888889 1.15240221459243 104.728095243702 Winsorized Mean ( 2 / 27 ) 120.701234567901 1.14135707322570 105.752386697684 Winsorized Mean ( 3 / 27 ) 120.712345679012 1.13585284040211 106.274634693239 Winsorized Mean ( 4 / 27 ) 120.717283950617 1.12699999195320 107.113828582556 Winsorized Mean ( 5 / 27 ) 120.995061728395 1.06976243646758 113.104608653046 Winsorized Mean ( 6 / 27 ) 121.113580246914 1.04081928953906 116.363696814795 Winsorized Mean ( 7 / 27 ) 121.096296296296 1.03791018136524 116.673194338464 Winsorized Mean ( 8 / 27 ) 121.066666666667 1.02636689947878 117.956518987653 Winsorized Mean ( 9 / 27 ) 121.033333333333 0.999089091295505 121.143684169738 Winsorized Mean ( 10 / 27 ) 121.107407407407 0.982953124514664 123.207713966222 Winsorized Mean ( 11 / 27 ) 121.120987654321 0.963581789133619 125.698709772446 Winsorized Mean ( 12 / 27 ) 121.061728395062 0.95446088444843 126.837810084822 Winsorized Mean ( 13 / 27 ) 121.077777777778 0.9320609713538 129.903280470928 Winsorized Mean ( 14 / 27 ) 121.285185185185 0.895224144480841 135.480243615995 Winsorized Mean ( 15 / 27 ) 121.285185185185 0.884140286741438 137.178666105342 Winsorized Mean ( 16 / 27 ) 121.245679012346 0.84323936195578 143.785601672024 Winsorized Mean ( 17 / 27 ) 121.161728395062 0.830958779677024 145.809553203294 Winsorized Mean ( 18 / 27 ) 121.228395061728 0.80851417329534 149.939727794290 Winsorized Mean ( 19 / 27 ) 121.251851851852 0.73870321625194 164.141497132047 Winsorized Mean ( 20 / 27 ) 121.004938271605 0.697831520476747 173.401365115947 Winsorized Mean ( 21 / 27 ) 120.979012345679 0.680213555902774 177.854456583296 Winsorized Mean ( 22 / 27 ) 120.951851851852 0.669252187955838 180.726868030550 Winsorized Mean ( 23 / 27 ) 120.895061728395 0.638888650324999 189.227123798328 Winsorized Mean ( 24 / 27 ) 121.072839506173 0.575253600397785 210.468634046709 Winsorized Mean ( 25 / 27 ) 120.980246913580 0.54729813278642 221.049990245065 Winsorized Mean ( 26 / 27 ) 121.108641975309 0.521871033010322 232.066227697511 Winsorized Mean ( 27 / 27 ) 121.508641975309 0.453427269444072 267.978240753551 Trimmed Mean ( 1 / 27 ) 120.768354430380 1.12772378521847 107.090367351775 Trimmed Mean ( 2 / 27 ) 120.851948051948 1.09887877112144 109.977507281003 Trimmed Mean ( 3 / 27 ) 120.933333333333 1.07196768361491 112.814346161556 Trimmed Mean ( 4 / 27 ) 121.015068493151 1.04274085478207 116.054787666723 Trimmed Mean ( 5 / 27 ) 121.1 1.01137394843920 119.738104967888 Trimmed Mean ( 6 / 27 ) 121.124637681159 0.991984942076913 122.103302725101 Trimmed Mean ( 7 / 27 ) 121.126865671642 0.976502731797657 124.041502115061 Trimmed Mean ( 8 / 27 ) 121.132307692308 0.958484650604164 126.378974995535 Trimmed Mean ( 9 / 27 ) 121.142857142857 0.939293331472368 128.972338122493 Trimmed Mean ( 10 / 27 ) 121.159016393443 0.921842942211313 131.431300111499 Trimmed Mean ( 11 / 27 ) 121.166101694915 0.903780003311798 134.065924506977 Trimmed Mean ( 12 / 27 ) 121.171929824561 0.885393001344236 136.856660986244 Trimmed Mean ( 13 / 27 ) 121.185454545455 0.864326359135494 140.207981932502 Trimmed Mean ( 14 / 27 ) 121.198113207547 0.84252234885294 143.851511324956 Trimmed Mean ( 15 / 27 ) 121.188235294118 0.822495709787123 147.342088052330 Trimmed Mean ( 16 / 27 ) 121.177551020408 0.799214459705955 151.620819104038 Trimmed Mean ( 17 / 27 ) 121.170212765957 0.777879389746143 155.769923156726 Trimmed Mean ( 18 / 27 ) 121.171111111111 0.75276340886059 160.968386195232 Trimmed Mean ( 19 / 27 ) 121.165116279070 0.72487738086248 167.152568803987 Trimmed Mean ( 20 / 27 ) 121.156097560976 0.703978664973347 172.101945114434 Trimmed Mean ( 21 / 27 ) 121.171794871795 0.685062806482164 176.876913657040 Trimmed Mean ( 22 / 27 ) 121.191891891892 0.663114165187072 182.761729811189 Trimmed Mean ( 23 / 27 ) 121.217142857143 0.635219616813456 190.827140171177 Trimmed Mean ( 24 / 27 ) 121.251515151515 0.604310921317419 200.644255919093 Trimmed Mean ( 25 / 27 ) 121.270967741935 0.579436017015491 209.29138710874 Trimmed Mean ( 26 / 27 ) 121.303448275862 0.551296786462661 220.03293190623 Trimmed Mean ( 27 / 27 ) 121.325925925926 0.51787403985572 234.276902467881 Median 121.2 Midrange 117.15 Midmean - Weighted Average at Xnp 120.9725 Midmean - Weighted Average at X(n+1)p 121.156097560976 Midmean - Empirical Distribution Function 121.156097560976 Midmean - Empirical Distribution Function - Averaging 121.156097560976 Midmean - Empirical Distribution Function - Interpolation 121.156097560976 Midmean - Closest Observation 120.964285714286 Midmean - True Basic - Statistics Graphics Toolkit 121.156097560976 Midmean - MS Excel (old versions) 121.156097560976 Number of observations 81

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t122907811973hw8vx6lbe9cuf/15o5k1229078053.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t122907811973hw8vx6lbe9cuf/15o5k1229078053.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t122907811973hw8vx6lbe9cuf/209vk1229078053.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t122907811973hw8vx6lbe9cuf/209vk1229078053.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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