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: Tue, 19 Oct 2010 20:45:27 +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/19/t1287521372lu3ojdbxlz5szzd.htm/, Retrieved Tue, 19 Oct 2010 22:49:34 +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/19/t1287521372lu3ojdbxlz5szzd.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 - Evi Van Dingenen

Dataseries X:

» Textbox « » Textfile « » CSV «

43,09 43,33 43,31 43,44 43,6 43,6 43,6 43,52 43,51 43,49 43,39 43,4 43,4 43,4 43,46 43,65 43,7 43,74 43,74 43,74 43,84 43,99 44,12 44,13 44,13 44,13 44,17 44,14 44,15 44,14 44,14 44,14 44,19 44,29 44,29 44,29 44,29 44,27 44,26 44,33 44,32 44,34 44,34 44,34 44,37 44,47 44,51 44,51 44,51 44,52 44,7 44,84 44,9 44,95 44,94 44,94 44,91 45,28 45,36 45,34 45,34 45,34 45,44 45,62 45,75 45,77 45,77 45,77 46,09 46,25 46,35 46,34 46,34 46,28 46,59 46,42 46,29 46,29 46,29 46,3 46,52 46,66 46,67 46,72 46,72 46,72 46,76 46,89 47,04 47,02 47,02 47,18 47,22 47,8 47,88 47,91

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 45.0134375 0.131302335273807 342.822824941633 Geometric Mean 44.9954013467979 Harmonic Mean 44.9775253139979 Quadratic Mean 45.0316264904456 Winsorized Mean ( 1 / 32 ) 45.0154166666667 0.130896195368652 343.901643129402 Winsorized Mean ( 2 / 32 ) 45.0141666666667 0.130460021659748 345.041845723955 Winsorized Mean ( 3 / 32 ) 44.9979166666667 0.126488671972738 355.7466132332 Winsorized Mean ( 4 / 32 ) 44.9966666666667 0.126127082482996 356.756580591903 Winsorized Mean ( 5 / 32 ) 44.989375 0.124832151561993 360.398939192021 Winsorized Mean ( 6 / 32 ) 44.988125 0.124616808490401 361.011692924757 Winsorized Mean ( 7 / 32 ) 44.9910416666667 0.124229509515078 362.160664098945 Winsorized Mean ( 8 / 32 ) 44.981875 0.122188766146354 368.134292690394 Winsorized Mean ( 9 / 32 ) 44.9725 0.119862585795920 375.200482297045 Winsorized Mean ( 10 / 32 ) 44.9704166666667 0.118942702985796 378.084704128819 Winsorized Mean ( 11 / 32 ) 44.9715625 0.118794966382541 378.564545867909 Winsorized Mean ( 12 / 32 ) 44.9815625 0.117533060683445 382.71412518687 Winsorized Mean ( 13 / 32 ) 44.9747916666667 0.116487328876332 386.091707145366 Winsorized Mean ( 14 / 32 ) 44.9733333333333 0.116264281019304 386.819863667898 Winsorized Mean ( 15 / 32 ) 44.9702083333333 0.113645047897169 395.707592767478 Winsorized Mean ( 16 / 32 ) 44.966875 0.110899068275158 405.475678915804 Winsorized Mean ( 17 / 32 ) 44.95625 0.107476053024310 418.290853961966 Winsorized Mean ( 18 / 32 ) 44.943125 0.105614878057522 425.537820301437 Winsorized Mean ( 19 / 32 ) 44.9411458333333 0.105337788927493 426.638401004103 Winsorized Mean ( 20 / 32 ) 44.9619791666667 0.102891168422226 436.985796314022 Winsorized Mean ( 21 / 32 ) 44.9860416666667 0.0980157836339344 458.967321372227 Winsorized Mean ( 22 / 32 ) 45.0135416666667 0.0946152155671215 475.75372942773 Winsorized Mean ( 23 / 32 ) 45.0159375 0.0943777611568892 476.976111196022 Winsorized Mean ( 24 / 32 ) 45.0159375 0.0943777611568892 476.976111196022 Winsorized Mean ( 25 / 32 ) 45.0133333333333 0.094008056143519 478.824211242204 Winsorized Mean ( 26 / 32 ) 45.0079166666667 0.0925906285123073 486.095811096953 Winsorized Mean ( 27 / 32 ) 44.9629166666667 0.0863179450994916 520.898830652671 Winsorized Mean ( 28 / 32 ) 44.8695833333333 0.0738840836827354 607.297013061801 Winsorized Mean ( 29 / 32 ) 44.8695833333333 0.0738840836827354 607.297013061801 Winsorized Mean ( 30 / 32 ) 44.8727083333333 0.0735600779597498 610.014420565004 Winsorized Mean ( 31 / 32 ) 44.8727083333333 0.0720662279420487 622.659317890445 Winsorized Mean ( 32 / 32 ) 44.8360416666667 0.065887244054472 680.49654087214 Trimmed Mean ( 1 / 32 ) 45.003085106383 0.128847470704064 349.274105735034 Trimmed Mean ( 2 / 32 ) 44.9902173913043 0.126501207979146 355.650496228629 Trimmed Mean ( 3 / 32 ) 44.9774444444444 0.124073350411862 362.506890441352 Trimmed Mean ( 4 / 32 ) 44.97 0.122960689829999 365.726640458621 Trimmed Mean ( 5 / 32 ) 44.9625581395349 0.121774295721223 369.228644462601 Trimmed Mean ( 6 / 32 ) 44.9564285714286 0.120740287184644 372.339917517987 Trimmed Mean ( 7 / 32 ) 44.950243902439 0.119566739637890 375.942708135822 Trimmed Mean ( 8 / 32 ) 44.94325 0.118259232385061 380.040095758964 Trimmed Mean ( 9 / 32 ) 44.9373076923077 0.117126585932053 383.664454442277 Trimmed Mean ( 10 / 32 ) 44.9323684210526 0.116208655114607 386.652512041719 Trimmed Mean ( 11 / 32 ) 44.9274324324324 0.115251935104724 389.819332678526 Trimmed Mean ( 12 / 32 ) 44.9220833333333 0.114105512475552 393.6889845086 Trimmed Mean ( 13 / 32 ) 44.9152857142857 0.112908970723854 397.800860519195 Trimmed Mean ( 14 / 32 ) 44.9088235294118 0.111619794230598 402.337451336218 Trimmed Mean ( 15 / 32 ) 44.9021212121212 0.110075734714927 407.920249893478 Trimmed Mean ( 16 / 32 ) 44.8953125 0.108608617444631 413.367866715437 Trimmed Mean ( 17 / 32 ) 44.8883870967742 0.107233662428952 418.603506399078 Trimmed Mean ( 18 / 32 ) 44.882 0.106062501560580 423.165580102449 Trimmed Mean ( 19 / 32 ) 44.8763793103448 0.104874164298543 427.906907392333 Trimmed Mean ( 20 / 32 ) 44.8705357142857 0.103393530042895 433.978177316030 Trimmed Mean ( 21 / 32 ) 44.8624074074074 0.101871013380837 440.384422600105 Trimmed Mean ( 22 / 32 ) 44.8515384615385 0.100652241163501 445.608939682533 Trimmed Mean ( 23 / 32 ) 44.8374 0.0994941532483806 450.653616681036 Trimmed Mean ( 24 / 32 ) 44.821875 0.0979187933600344 457.745377184091 Trimmed Mean ( 25 / 32 ) 44.805 0.0957642788384546 467.867565479001 Trimmed Mean ( 26 / 32 ) 44.7868181818182 0.0929256521153593 481.963991236985 Trimmed Mean ( 27 / 32 ) 44.767380952381 0.0893992464402771 500.757922856628 Trimmed Mean ( 28 / 32 ) 44.75 0.086259893523985 518.78107161768 Trimmed Mean ( 29 / 32 ) 44.7392105263158 0.0851351378089606 525.508170629953 Trimmed Mean ( 30 / 32 ) 44.7272222222222 0.0833996032793952 536.300179658919 Trimmed Mean ( 31 / 32 ) 44.7135294117647 0.0808652874558626 552.938483476856 Trimmed Mean ( 32 / 32 ) 44.698125 0.0775096735638059 576.678018946945 Median 44.51 Midrange 45.5 Midmean - Weighted Average at Xnp 44.8658823529412 Midmean - Weighted Average at X(n+1)p 44.8658823529412 Midmean - Empirical Distribution Function 44.8658823529412 Midmean - Empirical Distribution Function - Averaging 44.8658823529412 Midmean - Empirical Distribution Function - Interpolation 44.8658823529412 Midmean - Closest Observation 44.8658823529412 Midmean - True Basic - Statistics Graphics Toolkit 44.8658823529412 Midmean - MS Excel (old versions) 44.8658823529412 Number of observations 96

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/19/t1287521372lu3ojdbxlz5szzd/1c4t71287521125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/19/t1287521372lu3ojdbxlz5szzd/1c4t71287521125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/19/t1287521372lu3ojdbxlz5szzd/24vss1287521125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/19/t1287521372lu3ojdbxlz5szzd/24vss1287521125.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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