Opgave 5 oefening 2 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: Mon, 18 Oct 2010 15:56:23 +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/t12874174970832mtq15dcpxpk.htm/, Retrieved Mon, 18 Oct 2010 17:58:17 +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/t12874174970832mtq15dcpxpk.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 «

771,28 766,78 757,59 747,73 746,59 744,5 744,29 743,79 738,89 736,74 732,77 731,58 731,48 730,08 724,19 716,81 714,84 713,18 713,16 713,15 713,6 707,08 704,11 704,36 704,36 701,93 696,44 686,58 684,48 683,74 683,7 683,52 678,77 674,71 670,28 668,85 668,85 669,35 672,28 671,6 671,96 671,18 671,18 681,14 682,23 679,98 679,69 679,69 679,7 681,21 672,32 669,98 667,91 666,04 666,04 666,27 664,45 660,76 660,4 660,69 660,69 662,23 661,41 659,02 655,43 652,59 652,59 648,2 645,84 644,67 642,71 640,14 640,14 639,64 630,28 614,57 614,7 615,08 615,08 614,43 604,55 598,98 594,05 593,05 593,05 593,34 584,72 580,7 577,08 569,92 569,92 568,86 559,38 548,22 545,61 545,33

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 665.802395833333 5.44173519020985 122.351120104332 Geometric Mean 663.634756363864 Harmonic Mean 661.410266705074 Quadratic Mean 667.911682841408 Winsorized Mean ( 1 / 32 ) 665.7584375 5.43168513101219 122.569409205783 Winsorized Mean ( 2 / 32 ) 665.621354166667 5.38314911344902 123.649064913269 Winsorized Mean ( 3 / 32 ) 665.661979166667 5.2528722523546 126.723428095607 Winsorized Mean ( 4 / 32 ) 666.009479166667 5.16386444814455 128.975012000165 Winsorized Mean ( 5 / 32 ) 665.955833333333 5.1352602550822 129.682976179106 Winsorized Mean ( 6 / 32 ) 665.942708333333 5.13314933484711 129.733749184441 Winsorized Mean ( 7 / 32 ) 666.428333333333 5.02700086215714 132.56976706532 Winsorized Mean ( 8 / 32 ) 666.321666666667 4.90618947982936 135.812460852988 Winsorized Mean ( 9 / 32 ) 666.496979166667 4.80662072662745 138.662277943929 Winsorized Mean ( 10 / 32 ) 666.951145833333 4.59231830684188 145.231907126227 Winsorized Mean ( 11 / 32 ) 666.814791666667 4.5718660533823 145.85177778193 Winsorized Mean ( 12 / 32 ) 666.838541666667 4.56385138116566 146.113114992879 Winsorized Mean ( 13 / 32 ) 666.745104166667 4.51944588134953 147.528064650168 Winsorized Mean ( 14 / 32 ) 666.605104166667 4.27435770027332 155.954449980647 Winsorized Mean ( 15 / 32 ) 666.322291666667 3.97151080029047 167.775520494098 Winsorized Mean ( 16 / 32 ) 667.640625 3.66636612248883 182.098732831076 Winsorized Mean ( 17 / 32 ) 667.445833333333 3.6330122484071 183.716923504999 Winsorized Mean ( 18 / 32 ) 667.391458333333 3.61876719151498 184.425088162119 Winsorized Mean ( 19 / 32 ) 667.462708333333 3.60672709826863 185.060496718408 Winsorized Mean ( 20 / 32 ) 667.460625 3.60644926039699 185.074175957359 Winsorized Mean ( 21 / 32 ) 669.4578125 2.93896026490067 227.787296240504 Winsorized Mean ( 22 / 32 ) 670.979479166667 2.56503485394821 261.586885704054 Winsorized Mean ( 23 / 32 ) 671.099270833333 2.54967591355062 263.209636670559 Winsorized Mean ( 24 / 32 ) 671.036770833333 2.54110340247672 264.072988993403 Winsorized Mean ( 25 / 32 ) 671.138333333333 2.3785741465761 282.159937834783 Winsorized Mean ( 26 / 32 ) 670.182291666667 2.11265522879887 317.222745354287 Winsorized Mean ( 27 / 32 ) 667.738229166667 1.72702096205997 386.641646995526 Winsorized Mean ( 28 / 32 ) 667.8140625 1.56616987675463 426.399506472327 Winsorized Mean ( 29 / 32 ) 668.916666666667 1.3700655211207 488.23699038824 Winsorized Mean ( 30 / 32 ) 668.904166666667 1.36864249290741 488.735495305068 Winsorized Mean ( 31 / 32 ) 669.763125 1.24894300321277 536.263963429163 Winsorized Mean ( 32 / 32 ) 670.529791666667 1.05787605792413 633.845323035713 Trimmed Mean ( 1 / 32 ) 665.961914893617 5.2876999895959 125.945480304096 Trimmed Mean ( 2 / 32 ) 666.174239130435 5.12354884827049 130.022033332484 Trimmed Mean ( 3 / 32 ) 666.469111111111 4.96546667665436 134.220840559576 Trimmed Mean ( 4 / 32 ) 666.762613636364 4.84091812942517 137.734742833905 Trimmed Mean ( 5 / 32 ) 666.972790697674 4.72866090677943 141.048978526128 Trimmed Mean ( 6 / 32 ) 667.205238095238 4.60765687817002 144.80358580004 Trimmed Mean ( 7 / 32 ) 667.451585365854 4.46822238432756 149.377431997781 Trimmed Mean ( 8 / 32 ) 667.627 4.33214665778491 154.109971969732 Trimmed Mean ( 9 / 32 ) 667.82782051282 4.20053241256774 158.986470028114 Trimmed Mean ( 10 / 32 ) 668.014605263158 4.0677217272761 164.223280266147 Trimmed Mean ( 11 / 32 ) 668.152567567568 3.95503911914198 168.937031326385 Trimmed Mean ( 12 / 32 ) 668.314722222222 3.82609447643092 174.672822728006 Trimmed Mean ( 13 / 32 ) 668.483428571429 3.67469971666938 181.91511691119 Trimmed Mean ( 14 / 32 ) 668.672205882353 3.50230742856959 190.923332551492 Trimmed Mean ( 15 / 32 ) 668.88696969697 3.34295835073035 200.088334798079 Trimmed Mean ( 16 / 32 ) 669.1434375 3.20830501857288 208.566028986125 Trimmed Mean ( 17 / 32 ) 669.288870967742 3.103162782488 215.67958817524 Trimmed Mean ( 18 / 32 ) 669.462333333333 2.98109787502686 224.569055226777 Trimmed Mean ( 19 / 32 ) 669.65275862069 2.83374430092822 236.31375576171 Trimmed Mean ( 20 / 32 ) 669.850357142857 2.65275404507371 252.511294210182 Trimmed Mean ( 21 / 32 ) 670.062777777778 2.42261017727696 276.587122461005 Trimmed Mean ( 22 / 32 ) 670.115961538462 2.28478651437297 293.294781513697 Trimmed Mean ( 23 / 32 ) 670.0406 2.1892482245217 306.059674958232 Trimmed Mean ( 24 / 32 ) 669.948541666667 2.07036087386057 323.590225320199 Trimmed Mean ( 25 / 32 ) 669.853913043478 1.91789675658365 349.264844806708 Trimmed Mean ( 26 / 32 ) 669.741818181818 1.75808591840183 380.949424127485 Trimmed Mean ( 27 / 32 ) 669.703095238095 1.61771312641045 413.981369319852 Trimmed Mean ( 28 / 32 ) 669.87775 1.52982513193334 437.878641170857 Trimmed Mean ( 29 / 32 ) 670.063947368421 1.45254505342014 461.303383182985 Trimmed Mean ( 30 / 32 ) 670.169444444444 1.40116940641286 478.292946860827 Trimmed Mean ( 31 / 32 ) 670.288529411765 1.32880215800076 504.430644829959 Trimmed Mean ( 32 / 32 ) 670.339375 1.26411466034374 530.283680768104 Median 670.13 Midrange 658.305 Midmean - Weighted Average at Xnp 669.340204081633 Midmean - Weighted Average at X(n+1)p 669.340204081633 Midmean - Empirical Distribution Function 669.340204081633 Midmean - Empirical Distribution Function - Averaging 669.340204081633 Midmean - Empirical Distribution Function - Interpolation 669.340204081633 Midmean - Closest Observation 669.340204081633 Midmean - True Basic - Statistics Graphics Toolkit 669.340204081633 Midmean - MS Excel (old versions) 670.713529411765 Number of observations 96

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/18/t12874174970832mtq15dcpxpk/1gepm1287417379.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t12874174970832mtq15dcpxpk/1gepm1287417379.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t12874174970832mtq15dcpxpk/2r56p1287417379.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t12874174970832mtq15dcpxpk/2r56p1287417379.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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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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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