Iko - Paper - Ishia Opgenhaffen (opgave 5, oef2)

*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 09:42:43 -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/t1268581468m39jfpx8ns9y4ac.htm/, Retrieved Sun, 14 Mar 2010 16:44:30 +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/t1268581468m39jfpx8ns9y4ac.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 «

121,67 121,65 121,61 121,5 121,41 121,41 121,4 121,38 121,34 121,19 120,96 120,96 120,96 120,9 120,86 120,73 120,53 120,53 120,53 120,52 120,51 120,43 120,29 120,27 120,27 120,24 120,21 120,06 119,86 119,85 119,85 119,83 119,71 119,57 119,2 119,13 119,13 119,09 118,9 118,54 118,12 118,11 118,1 118,08 117,91 117,63 117,28 117,2 117,17 117,14 116,96 116,34 115,99 115,99 115,97 115,92 115,63 115,31 115,13 115,09 115,07 115,01 114,64 113,86 113,34 113,33 113,32 113,26 113,2 112,61 112,28 112,16

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 118.251805555556 0.332054314145444 356.121876807659 Geometric Mean 118.218353473916 Harmonic Mean 118.184553072207 Quadratic Mean 118.284901749735 Winsorized Mean ( 1 / 24 ) 118.253194444444 0.331587377362071 356.627551341678 Winsorized Mean ( 2 / 24 ) 118.26125 0.329156218262889 359.286087998336 Winsorized Mean ( 3 / 24 ) 118.28125 0.322806122226559 366.415758115595 Winsorized Mean ( 4 / 24 ) 118.279583333333 0.321375871226227 368.04126856827 Winsorized Mean ( 5 / 24 ) 118.28375 0.320463062203882 369.102601674406 Winsorized Mean ( 6 / 24 ) 118.28375 0.320166992170628 369.443924241143 Winsorized Mean ( 7 / 24 ) 118.282777777778 0.319689257759298 369.992969444209 Winsorized Mean ( 8 / 24 ) 118.336111111111 0.30684602299728 385.653071058901 Winsorized Mean ( 9 / 24 ) 118.414861111111 0.285127637526354 415.304746107491 Winsorized Mean ( 10 / 24 ) 118.434305555556 0.271481389799356 436.252023179515 Winsorized Mean ( 11 / 24 ) 118.443472222222 0.269860144596631 438.906873037008 Winsorized Mean ( 12 / 24 ) 118.446805555556 0.269274065144027 439.874540060892 Winsorized Mean ( 13 / 24 ) 118.443194444444 0.266592773388040 444.285090474092 Winsorized Mean ( 14 / 24 ) 118.470416666667 0.259517989273674 456.501751567340 Winsorized Mean ( 15 / 24 ) 118.51 0.244784565624704 484.14000162778 Winsorized Mean ( 16 / 24 ) 118.53 0.228680470161949 518.321481130674 Winsorized Mean ( 17 / 24 ) 118.541805555556 0.226788779450612 522.696959888046 Winsorized Mean ( 18 / 24 ) 118.546805555556 0.225991107542180 524.564027517894 Winsorized Mean ( 19 / 24 ) 118.544166666667 0.225665313516654 525.309649140732 Winsorized Mean ( 20 / 24 ) 118.638611111111 0.210069694221194 564.758336755562 Winsorized Mean ( 21 / 24 ) 118.796111111111 0.180128796247846 659.506495272722 Winsorized Mean ( 22 / 24 ) 118.808333333333 0.16689678948727 711.86709881196 Winsorized Mean ( 23 / 24 ) 118.811527777778 0.164751990273233 721.1538238824 Winsorized Mean ( 24 / 24 ) 118.821527777778 0.163351256528612 727.398921213472 Trimmed Mean ( 1 / 24 ) 118.29 0.326456982603655 362.344830417101 Trimmed Mean ( 2 / 24 ) 118.328970588235 0.320241975272346 369.498628303188 Trimmed Mean ( 3 / 24 ) 118.365909090909 0.314260294564851 376.649265395768 Trimmed Mean ( 4 / 24 ) 118.39765625 0.309851774454039 382.110628408108 Trimmed Mean ( 5 / 24 ) 118.431935483871 0.304887981155153 388.444093582038 Trimmed Mean ( 6 / 24 ) 118.4675 0.299002827207313 396.208628214277 Trimmed Mean ( 7 / 24 ) 118.505517241379 0.291754105543106 406.182860805948 Trimmed Mean ( 8 / 24 ) 118.546428571429 0.282825083451439 419.151042491544 Trimmed Mean ( 9 / 24 ) 118.581481481481 0.275061953177412 431.108265289594 Trimmed Mean ( 10 / 24 ) 118.607115384615 0.270580117600329 438.343794202236 Trimmed Mean ( 11 / 24 ) 118.632 0.267761849715872 443.050420087413 Trimmed Mean ( 12 / 24 ) 118.657708333333 0.264237367697841 449.057260020165 Trimmed Mean ( 13 / 24 ) 118.685217391304 0.259554754237685 457.264663634785 Trimmed Mean ( 14 / 24 ) 118.715681818182 0.253795167555973 467.761789798459 Trimmed Mean ( 15 / 24 ) 118.745714285714 0.247675404557855 479.440881494458 Trimmed Mean ( 16 / 24 ) 118.774 0.242787973342997 489.208746069982 Trimmed Mean ( 17 / 24 ) 118.802894736842 0.239569287498972 495.902024742433 Trimmed Mean ( 18 / 24 ) 118.833611111111 0.23511738128135 505.422484988086 Trimmed Mean ( 19 / 24 ) 118.867352941176 0.228633197125272 519.904171554085 Trimmed Mean ( 20 / 24 ) 118.905625 0.219036534688224 542.857497125992 Trimmed Mean ( 21 / 24 ) 118.937666666667 0.210106532000488 566.082670225553 Trimmed Mean ( 22 / 24 ) 118.955 0.206569677702299 575.85896111739 Trimmed Mean ( 23 / 24 ) 118.973461538462 0.204465488761978 581.875514830578 Trimmed Mean ( 24 / 24 ) 118.994583333333 0.200677276399908 592.964910965814 Median 119.13 Midrange 116.915 Midmean - Weighted Average at Xnp 118.847179487179 Midmean - Weighted Average at X(n+1)p 118.922894736842 Midmean - Empirical Distribution Function 118.847179487179 Midmean - Empirical Distribution Function - Averaging 118.922894736842 Midmean - Empirical Distribution Function - Interpolation 118.922894736842 Midmean - Closest Observation 118.847179487179 Midmean - True Basic - Statistics Graphics Toolkit 118.922894736842 Midmean - MS Excel (old versions) 118.847179487179 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/14/t1268581468m39jfpx8ns9y4ac/1ugr51268581361.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268581468m39jfpx8ns9y4ac/1ugr51268581361.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268581468m39jfpx8ns9y4ac/25vt81268581361.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268581468m39jfpx8ns9y4ac/25vt81268581361.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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