Centrummaten Indexcijfers Consumptieprijzen

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 18 Oct 2010 14:16:36 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Oct/18/t128741141826mcouo3te0tm6x.htm/, Retrieved Mon, 18 Oct 2010 16:17:00 +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/2010/Oct/18/t128741141826mcouo3te0tm6x.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

95,05 96,84 96,92 97,44 97,78 97,69 96,67 98,29 98,2 98,71 98,54 98,2 96,92 99,06 99,65 99,82 99,99 100,33 99,31 101,1 101,1 100,93 100,85 100,93 99,6 101,88 101,81 102,38 102,74 102,82 101,72 103,47 102,98 102,68 102,9 103,03 101,29 103,69 103,68 104,2 104,08 104,16 103,05 104,66 104,46 104,95 105,85 106,23 104,86 107,44 108,23 108,45 109,39 110,15 109,13 110,28 110,17 109,99 109,26 109,11 107,06 109,53 108,92 109,24 109,12 109 107,23 109,49 109,04 109,02 109,23 109,46

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 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 103.630972222222 0.519121502708587 199.627585606671 Geometric Mean 103.538595894003 Harmonic Mean 103.446218992539 Quadratic Mean 103.723247106315 Winsorized Mean ( 1 / 24 ) 103.651944444444 0.514073822622004 201.628520813944 Winsorized Mean ( 2 / 24 ) 103.656111111111 0.513081250050312 202.026698697227 Winsorized Mean ( 3 / 24 ) 103.652777777778 0.511284140100128 202.730281751902 Winsorized Mean ( 4 / 24 ) 103.627222222222 0.506957432251575 204.410105523017 Winsorized Mean ( 5 / 24 ) 103.660555555556 0.499971669341697 207.332858863870 Winsorized Mean ( 6 / 24 ) 103.678888888889 0.495963974802465 209.045201176522 Winsorized Mean ( 7 / 24 ) 103.680833333333 0.493369643616798 210.148384025553 Winsorized Mean ( 8 / 24 ) 103.713055555556 0.483344124814322 214.573944796365 Winsorized Mean ( 9 / 24 ) 103.710555555556 0.482940502856462 214.748100319058 Winsorized Mean ( 10 / 24 ) 103.721666666667 0.480717341848933 215.764353887740 Winsorized Mean ( 11 / 24 ) 103.744583333333 0.4722534024388 219.679906587391 Winsorized Mean ( 12 / 24 ) 103.77125 0.467626567164941 221.910509980495 Winsorized Mean ( 13 / 24 ) 103.832638888889 0.457877280280607 226.769580760276 Winsorized Mean ( 14 / 24 ) 103.867638888889 0.448620363512101 231.526803811899 Winsorized Mean ( 15 / 24 ) 103.923888888889 0.439431431069422 236.496257529815 Winsorized Mean ( 16 / 24 ) 103.930555555556 0.437169409588015 237.735196644932 Winsorized Mean ( 17 / 24 ) 103.951805555556 0.428591714618868 242.542732418419 Winsorized Mean ( 18 / 24 ) 103.876805555556 0.403857225154416 257.211705240232 Winsorized Mean ( 19 / 24 ) 103.908472222222 0.382614382936425 271.574924666352 Winsorized Mean ( 20 / 24 ) 103.833472222222 0.329454376534315 315.1679856692 Winsorized Mean ( 21 / 24 ) 103.795555555556 0.317086569199241 327.341381306932 Winsorized Mean ( 22 / 24 ) 103.743611111111 0.309200424333921 335.522214546100 Winsorized Mean ( 23 / 24 ) 103.532777777778 0.262935697154486 393.757024619399 Winsorized Mean ( 24 / 24 ) 103.406111111111 0.244873938022236 422.28304059749 Trimmed Mean ( 1 / 24 ) 103.658571428571 0.510697622395347 202.974454712315 Trimmed Mean ( 2 / 24 ) 103.665588235294 0.506429269513407 204.699045801399 Trimmed Mean ( 3 / 24 ) 103.670757575758 0.50170851736032 206.635434696642 Trimmed Mean ( 4 / 24 ) 103.6775 0.496598948723229 208.775109706853 Trimmed Mean ( 5 / 24 ) 103.692096774194 0.491709379686568 210.880859828809 Trimmed Mean ( 6 / 24 ) 103.699666666667 0.487614101765991 212.667489088395 Trimmed Mean ( 7 / 24 ) 103.703965517241 0.483358382624057 214.548809424289 Trimmed Mean ( 8 / 24 ) 103.708214285714 0.478421722562496 216.771541497401 Trimmed Mean ( 9 / 24 ) 103.707407407407 0.474290170655893 218.658141837498 Trimmed Mean ( 10 / 24 ) 103.706923076923 0.468812042728593 221.212156738392 Trimmed Mean ( 11 / 24 ) 103.7048 0.462036948783121 224.451313413635 Trimmed Mean ( 12 / 24 ) 103.699375 0.454933594079579 227.943982043807 Trimmed Mean ( 13 / 24 ) 103.69 0.446473568470739 232.242191525825 Trimmed Mean ( 14 / 24 ) 103.672045454545 0.437296322815231 237.075045102425 Trimmed Mean ( 15 / 24 ) 103.648095238095 0.426977225929981 242.748533044927 Trimmed Mean ( 16 / 24 ) 103.615 0.414982854140709 249.685014612355 Trimmed Mean ( 17 / 24 ) 103.577631578947 0.399035364980416 259.570054859751 Trimmed Mean ( 18 / 24 ) 103.533611111111 0.379165573578284 273.056464842094 Trimmed Mean ( 19 / 24 ) 103.493235294118 0.358699304202967 288.523657786514 Trimmed Mean ( 20 / 24 ) 103.4440625 0.335773619066610 308.076801231603 Trimmed Mean ( 21 / 24 ) 103.397333333333 0.319985248702144 323.131562322674 Trimmed Mean ( 22 / 24 ) 103.348571428571 0.300432102518579 343.999760885008 Trimmed Mean ( 23 / 24 ) 103.298846153846 0.273292363552902 377.979262980213 Trimmed Mean ( 24 / 24 ) 103.268333333333 0.252159992535986 409.534963475999 Median 103.04 Midrange 102.665 Midmean - Weighted Average at Xnp 103.433243243243 Midmean - Weighted Average at X(n+1)p 103.533611111111 Midmean - Empirical Distribution Function 103.433243243243 Midmean - Empirical Distribution Function - Averaging 103.533611111111 Midmean - Empirical Distribution Function - Interpolation 103.533611111111 Midmean - Closest Observation 103.433243243243 Midmean - True Basic - Statistics Graphics Toolkit 103.533611111111 Midmean - MS Excel (old versions) 103.577631578947 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/18/t128741141826mcouo3te0tm6x/149lp1287411394.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t128741141826mcouo3te0tm6x/149lp1287411394.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t128741141826mcouo3te0tm6x/2ej3a1287411394.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t128741141826mcouo3te0tm6x/2ej3a1287411394.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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