opdracht 5

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 15 Oct 2010 13:54:55 +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/15/t1287150927lfdlrpx4x1wuhnt.htm/, Retrieved Fri, 15 Oct 2010 15:55:29 +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/2010/Oct/15/t1287150927lfdlrpx4x1wuhnt.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 «

108 106,6 122,2 115,8 115,6 124,5 121,7 118,7 113,7 113,4 115,1 143,9 101 103,4 121,5 111,9 117,4 124,3 122 119,7 115 112,2 115,3 142,6 104,1 105,3 124,4 113,9 124,8 131,8 125,6 125 119,7 116,1 120 148,1 109,2 109,4 135,1 114,9 129 138,5 125,6 130,4 120,3 126,2 127,6 150,9 114,6 118,6 131,4 124,5 136,8 136,8 136,6 131 125,8 129,4 124,8 157,1 116,6 114,2 128,4 127,3 133,5 137,2 137,7 131,2 127,7 133,9 124,3 160,6

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 2 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 124.186111111111 1.43142725314519 86.756844148555 Geometric Mean 123.617297430520 Harmonic Mean 123.063534373882 Quadratic Mean 124.770461470476 Winsorized Mean ( 1 / 24 ) 124.170833333333 1.40743392607248 88.2249823832506 Winsorized Mean ( 2 / 24 ) 124.018055555556 1.35079430407176 91.8112070666291 Winsorized Mean ( 3 / 24 ) 123.951388888889 1.30905715908713 94.6875298977216 Winsorized Mean ( 4 / 24 ) 123.790277777778 1.23762759529712 100.022234675576 Winsorized Mean ( 5 / 24 ) 123.797222222222 1.19877998137645 103.269343954240 Winsorized Mean ( 6 / 24 ) 123.555555555556 1.11004780890867 111.306517218414 Winsorized Mean ( 7 / 24 ) 123.497222222222 1.09200926821661 113.091734490412 Winsorized Mean ( 8 / 24 ) 123.719444444444 1.03413122097459 119.636117675519 Winsorized Mean ( 9 / 24 ) 123.706944444444 1.01901584665361 121.398450132734 Winsorized Mean ( 10 / 24 ) 123.873611111111 0.99337593461826 124.699629610731 Winsorized Mean ( 11 / 24 ) 123.888888888889 0.981032071990356 126.284239247692 Winsorized Mean ( 12 / 24 ) 123.672222222222 0.931695457201317 132.738891519034 Winsorized Mean ( 13 / 24 ) 123.509722222222 0.887083808213349 139.231176444286 Winsorized Mean ( 14 / 24 ) 123.509722222222 0.862921121982188 143.129793762044 Winsorized Mean ( 15 / 24 ) 123.218055555556 0.79801280575013 154.406113119615 Winsorized Mean ( 16 / 24 ) 123.151388888889 0.781408065213118 157.601891215829 Winsorized Mean ( 17 / 24 ) 123.127777777778 0.770949514711597 159.709261667852 Winsorized Mean ( 18 / 24 ) 123.127777777778 0.756286181307621 162.805801323633 Winsorized Mean ( 19 / 24 ) 123.048611111111 0.721793521946388 170.476192110035 Winsorized Mean ( 20 / 24 ) 122.826388888889 0.674670246514479 182.053958246183 Winsorized Mean ( 21 / 24 ) 122.797222222222 0.645966697489387 190.098379219061 Winsorized Mean ( 22 / 24 ) 122.766666666667 0.599190899429649 204.887401967427 Winsorized Mean ( 23 / 24 ) 122.798611111111 0.53312603459403 230.336924372154 Winsorized Mean ( 24 / 24 ) 123.165277777778 0.472975298209166 260.405307093458 Trimmed Mean ( 1 / 24 ) 123.997142857143 1.33501494075676 92.8807154673898 Trimmed Mean ( 2 / 24 ) 123.813235294118 1.24712118789428 99.2792332420972 Trimmed Mean ( 3 / 24 ) 123.701515151515 1.17895986005808 104.924280581886 Trimmed Mean ( 4 / 24 ) 123.6078125 1.11674729783409 110.685571158072 Trimmed Mean ( 5 / 24 ) 123.554838709677 1.06965173073421 115.509408492117 Trimmed Mean ( 6 / 24 ) 123.496666666667 1.02542802601394 120.434261141394 Trimmed Mean ( 7 / 24 ) 123.484482758621 0.998004062939579 123.731442931106 Trimmed Mean ( 8 / 24 ) 123.482142857143 0.969060688404375 127.424571375880 Trimmed Mean ( 9 / 24 ) 123.442592592593 0.947605765387564 130.267878374617 Trimmed Mean ( 10 / 24 ) 123.401923076923 0.924170535870495 133.527220666788 Trimmed Mean ( 11 / 24 ) 123.334 0.900175085010394 137.011123784409 Trimmed Mean ( 12 / 24 ) 123.258333333333 0.872195776654094 141.319571399641 Trimmed Mean ( 13 / 24 ) 123.204347826087 0.8479184887093 145.302112722684 Trimmed Mean ( 14 / 24 ) 123.165909090909 0.82659253162514 149.004381697904 Trimmed Mean ( 15 / 24 ) 123.123809523810 0.803764441051791 153.183946981646 Trimmed Mean ( 16 / 24 ) 123.1125 0.788362368685222 156.162324446458 Trimmed Mean ( 17 / 24 ) 123.107894736842 0.770669487627473 159.741493225368 Trimmed Mean ( 18 / 24 ) 123.105555555556 0.748256645179095 164.523170423819 Trimmed Mean ( 19 / 24 ) 123.102941176471 0.720349554854147 170.893339694499 Trimmed Mean ( 20 / 24 ) 123.109375 0.69027459728521 178.348407263107 Trimmed Mean ( 21 / 24 ) 123.143333333333 0.660575912668989 186.418140552212 Trimmed Mean ( 22 / 24 ) 123.185714285714 0.625382724843055 196.976522363372 Trimmed Mean ( 23 / 24 ) 123.238461538462 0.588402711991787 209.445774172743 Trimmed Mean ( 24 / 24 ) 123.295833333333 0.556531675683107 221.543244923113 Median 124.35 Midrange 130.8 Midmean - Weighted Average at Xnp 122.889189189189 Midmean - Weighted Average at X(n+1)p 123.105555555556 Midmean - Empirical Distribution Function 122.889189189189 Midmean - Empirical Distribution Function - Averaging 123.105555555556 Midmean - Empirical Distribution Function - Interpolation 123.105555555556 Midmean - Closest Observation 122.889189189189 Midmean - True Basic - Statistics Graphics Toolkit 123.105555555556 Midmean - MS Excel (old versions) 123.107894736842 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/15/t1287150927lfdlrpx4x1wuhnt/1rhxp1287150893.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/15/t1287150927lfdlrpx4x1wuhnt/1rhxp1287150893.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/15/t1287150927lfdlrpx4x1wuhnt/2krfa1287150893.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/15/t1287150927lfdlrpx4x1wuhnt/2krfa1287150893.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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