Opdracht 5 oefening2 stap 1

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 17 Oct 2010 10:44:05 +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/17/t1287312190gzz190wc7z4zfam.htm/, Retrieved Sun, 17 Oct 2010 12:43:12 +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/17/t1287312190gzz190wc7z4zfam.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 «

0,74 0,73 0,76 0,8 0,83 0,81 0,83 0,88 0,89 0,93 0,91 0,9 0,86 0,88 0,93 0,98 0,97 1,03 1,06 1,06 1,08 1,09 1,04 1 1,01 1,02 1,04 1,06 1,06 1,06 1,06 1,06 1,02 0,98 0,99 0,99 0,94 0,96 0,98 1,01 1,01 1,02 1,04 1,03 1,05 1,08 1,17 1,11 1,11 1,11 1,2 1,21 1,31 1,37 1,37 1,26 1,23 1,17 1,06 0,95 0,92 0,92 0,9 0,93 0,93 0,97 0,96 0,99 0,98 0,96 1 0,99 1,03 1,02 1,07 1,13 1,15 1,16

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 1.01410256410256 0.0144397376669605 70.2299853011128 Geometric Mean 1.00626132334733 Harmonic Mean 0.998430026892108 Quadratic Mean 1.02198775646236 Winsorized Mean ( 1 / 26 ) 1.01423076923077 0.0144075118587844 70.3959697671449 Winsorized Mean ( 2 / 26 ) 1.01320512820513 0.0138211948674450 73.3080705338776 Winsorized Mean ( 3 / 26 ) 1.01282051282051 0.0129664356221684 78.1109429247402 Winsorized Mean ( 4 / 26 ) 1.01179487179487 0.0124927465998146 80.9905863142928 Winsorized Mean ( 5 / 26 ) 1.01179487179487 0.011947748921331 84.6849794431533 Winsorized Mean ( 6 / 26 ) 1.01102564102564 0.0117847688709756 85.790875671365 Winsorized Mean ( 7 / 26 ) 1.01102564102564 0.0107286790224189 94.2357991056471 Winsorized Mean ( 8 / 26 ) 1.01307692307692 0.0103699591942254 97.6934338990518 Winsorized Mean ( 9 / 26 ) 1.01192307692308 0.0101471978456848 99.724386211057 Winsorized Mean ( 10 / 26 ) 1.01192307692308 0.0096940505016459 104.385991877314 Winsorized Mean ( 11 / 26 ) 1.01051282051282 0.00896007616587881 112.779490018287 Winsorized Mean ( 12 / 26 ) 1.00743589743590 0.00845043116026645 119.217100089853 Winsorized Mean ( 13 / 26 ) 1.00910256410256 0.00818164148101545 123.337421524039 Winsorized Mean ( 14 / 26 ) 1.01089743589744 0.00790634889787747 127.858945886997 Winsorized Mean ( 15 / 26 ) 1.00705128205128 0.00730868539910127 137.788292566966 Winsorized Mean ( 16 / 26 ) 1.00705128205128 0.0067001547547969 150.302689849110 Winsorized Mean ( 17 / 26 ) 1.00705128205128 0.0067001547547969 150.302689849110 Winsorized Mean ( 18 / 26 ) 1.00474358974359 0.0063835775160883 157.395063694515 Winsorized Mean ( 19 / 26 ) 1.00230769230769 0.00607129107539029 165.089711539363 Winsorized Mean ( 20 / 26 ) 1.00487179487179 0.00568264848736533 176.831594828715 Winsorized Mean ( 21 / 26 ) 1.00756410256410 0.00529259089635065 190.372564646710 Winsorized Mean ( 22 / 26 ) 1.01038461538462 0.00490482954887392 205.997905802167 Winsorized Mean ( 23 / 26 ) 1.01038461538462 0.00490482954887392 205.997905802167 Winsorized Mean ( 24 / 26 ) 1.01038461538462 0.00490482954887392 205.997905802167 Winsorized Mean ( 25 / 26 ) 1.01358974358974 0.00448839239589327 225.824672663902 Winsorized Mean ( 26 / 26 ) 1.01358974358974 0.00448839239589327 225.824672663902 Trimmed Mean ( 1 / 26 ) 1.01315789473684 0.0135390410481063 74.8323231414199 Trimmed Mean ( 2 / 26 ) 1.01202702702703 0.0124906180707789 81.0229743069808 Trimmed Mean ( 3 / 26 ) 1.01138888888889 0.0116218211793870 87.0249914602659 Trimmed Mean ( 4 / 26 ) 1.01085714285714 0.0109954684005517 91.9339773471065 Trimmed Mean ( 5 / 26 ) 1.01058823529412 0.0104294998329984 96.897094920762 Trimmed Mean ( 6 / 26 ) 1.01030303030303 0.00993209977393165 101.720990857817 Trimmed Mean ( 7 / 26 ) 1.01015625 0.00937927729806133 107.700862006585 Trimmed Mean ( 8 / 26 ) 1.01 0.00900378908427672 112.174995498702 Trimmed Mean ( 9 / 26 ) 1.0095 0.00863714550565612 116.878892376992 Trimmed Mean ( 10 / 26 ) 1.00913793103448 0.0082434394628562 122.417097327095 Trimmed Mean ( 11 / 26 ) 1.00875 0.00786684023764785 128.228102964706 Trimmed Mean ( 12 / 26 ) 1.00851851851852 0.00757172739365253 133.195302219144 Trimmed Mean ( 13 / 26 ) 1.00865384615385 0.00731755902930403 137.840206292095 Trimmed Mean ( 14 / 26 ) 1.0086 0.00705668014677423 142.928399618772 Trimmed Mean ( 15 / 26 ) 1.00833333333333 0.0067852921179044 148.605736615618 Trimmed Mean ( 16 / 26 ) 1.00847826086957 0.00657154891927982 153.461272716218 Trimmed Mean ( 17 / 26 ) 1.00863636363636 0.00642562678716392 156.970891252392 Trimmed Mean ( 18 / 26 ) 1.00880952380952 0.00623021729507331 161.922044774789 Trimmed Mean ( 19 / 26 ) 1.00925 0.0060382063477026 167.144006329627 Trimmed Mean ( 20 / 26 ) 1.01 0.00584289333810359 172.859564868903 Trimmed Mean ( 21 / 26 ) 1.01055555555556 0.00567568532250253 178.049961922480 Trimmed Mean ( 22 / 26 ) 1.01088235294118 0.00554302000510317 182.370323760425 Trimmed Mean ( 23 / 26 ) 1.0109375 0.00545064688007675 185.471105034375 Trimmed Mean ( 24 / 26 ) 1.011 0.00530343631823832 190.631119020551 Trimmed Mean ( 25 / 26 ) 1.01107142857143 0.00507455749665408 199.243269829553 Trimmed Mean ( 26 / 26 ) 1.01076923076923 0.0048650425541052 207.761642273062 Median 1.01 Midrange 1.05 Midmean - Weighted Average at Xnp 1.00372093023256 Midmean - Weighted Average at X(n+1)p 1.00372093023256 Midmean - Empirical Distribution Function 1.00372093023256 Midmean - Empirical Distribution Function - Averaging 1.00372093023256 Midmean - Empirical Distribution Function - Interpolation 1.01128205128205 Midmean - Closest Observation 1.00372093023256 Midmean - True Basic - Statistics Graphics Toolkit 1.00372093023256 Midmean - MS Excel (old versions) 1.00372093023256 Number of observations 78

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/17/t1287312190gzz190wc7z4zfam/16jc81287312243.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/17/t1287312190gzz190wc7z4zfam/16jc81287312243.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/17/t1287312190gzz190wc7z4zfam/26jc81287312243.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/17/t1287312190gzz190wc7z4zfam/26jc81287312243.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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