workshop 3 deel 2.4 central tendency

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Wed, 21 Oct 2009 09:23:57 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138708ydbkc4j2j7y64qk.htm/, Retrieved Wed, 21 Oct 2009 17:25:10 +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/2009/Oct/21/t1256138708ydbkc4j2j7y64qk.htm/}, year = {2009}, } @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 = {2009}, 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:

workshop 3 deel 2.4 central tendency

Dataseries X:

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0,92705025 0,921070695 0,949104768 0,928945683 0,922979649 0,906730594 0,914614988 0,909161955 0,903639 0,903768494 0,900103806 0,915456756 0,948106005 0,93403488 0,931332588 0,923751291 0,9228621 0,934802157 0,942641343 0,960760531 0,982820498 1,003007225 1,031049528 1,08088491 1,082222064 1,08401642 1,0767526 1,078429482 1,080280055 1,08004402 1,091126624 1,083699255 1,06503446 1,05183308 1,034373004 1,0342178 1,009174176 1,01661552 1,030036554 1,05131403 1,066615344 1,063020192 1,067798 1,080772623 1,069072968 1,072696102 1,056834175 1,056627752 1,029580945 1,071080968 1,064087256 1,05000896 1,05544213 1,049496917 1,051364638 1,062857412 1,06406726 1,081659085 1,093903324 1,06348812 1,071258266 1,078983234 1,067478475 1,069441751 1,069204092 1,073095034 1,074490134 1,071738855 1,0829616 1,096770604 1,11241925 1,124652816 1,117678166 1,11727848 1,110210378 1,134913325 1,162971484 1,16872056 1,195685888 1,210769175

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 1.0378630572 0.00838056667646941 123.841632346183 Geometric Mean 1.03512986679879 Harmonic Mean 1.03233736710047 Quadratic Mean 1.04053265370589 Winsorized Mean ( 1 / 26 ) 1.0377187060375 0.00832419241742798 124.662988792147 Winsorized Mean ( 2 / 26 ) 1.0370478101875 0.00817371578114256 126.875932312212 Winsorized Mean ( 3 / 26 ) 1.0369432985875 0.00810776666628423 127.895059301544 Winsorized Mean ( 4 / 26 ) 1.0356619586875 0.00783200186789263 132.234641430974 Winsorized Mean ( 5 / 26 ) 1.0353614914375 0.00766440548095406 135.086993245642 Winsorized Mean ( 6 / 26 ) 1.0349015252875 0.00757705844667917 136.583547899260 Winsorized Mean ( 7 / 26 ) 1.035357772425 0.00747566499362757 138.497079966473 Winsorized Mean ( 8 / 26 ) 1.035050989925 0.00737510919001126 140.343819089060 Winsorized Mean ( 9 / 26 ) 1.0348157160875 0.00733990544975841 140.984883684239 Winsorized Mean ( 10 / 26 ) 1.0332321995875 0.00711684749056702 145.181163563922 Winsorized Mean ( 11 / 26 ) 1.03329155545 0.00698507679759298 147.928445941506 Winsorized Mean ( 12 / 26 ) 1.0331593654 0.00688539848781328 150.050772984109 Winsorized Mean ( 13 / 26 ) 1.0323918293125 0.00669313395252256 154.246401855353 Winsorized Mean ( 14 / 26 ) 1.0328092265375 0.00659771138329946 156.540528455338 Winsorized Mean ( 15 / 26 ) 1.0328147806625 0.00655702228604912 157.512775709172 Winsorized Mean ( 16 / 26 ) 1.0342347106625 0.00624883045490018 165.508524855476 Winsorized Mean ( 17 / 26 ) 1.0352763183 0.00602306247077022 171.885369498353 Winsorized Mean ( 18 / 26 ) 1.0353268506 0.00596500882886122 173.566692071042 Winsorized Mean ( 19 / 26 ) 1.03806842615 0.00546088562280001 190.091589140031 Winsorized Mean ( 20 / 26 ) 1.0434602759 0.00447964093665931 232.933909358851 Winsorized Mean ( 21 / 26 ) 1.04869733255 0.00358908359818983 292.190834752056 Winsorized Mean ( 22 / 26 ) 1.050101527925 0.00328628723992296 319.540396581285 Winsorized Mean ( 23 / 26 ) 1.052081710625 0.00293591246657695 358.349141059933 Winsorized Mean ( 24 / 26 ) 1.055468273525 0.00230119017456342 458.661906865322 Winsorized Mean ( 25 / 26 ) 1.0549036307125 0.00219959662742122 479.589583636185 Winsorized Mean ( 26 / 26 ) 1.0547794397625 0.00210194536890781 501.811062915765 Trimmed Mean ( 1 / 26 ) 1.03741245634615 0.00810959993337186 127.923999318030 Trimmed Mean ( 2 / 26 ) 1.03709008825 0.0078587814927764 131.965762020902 Trimmed Mean ( 3 / 26 ) 1.03711294125676 0.00765960954027958 135.400236239575 Trimmed Mean ( 4 / 26 ) 1.037175771875 0.00745478106211656 139.128937957103 Trimmed Mean ( 5 / 26 ) 1.03760828992857 0.00731061514413391 141.931734809095 Trimmed Mean ( 6 / 26 ) 1.03813694839706 0.00718830958369952 144.420177833072 Trimmed Mean ( 7 / 26 ) 1.03879056922727 0.0070630075589171 147.074820543805 Trimmed Mean ( 8 / 26 ) 1.03940356865625 0.00693594729134831 149.857478004882 Trimmed Mean ( 9 / 26 ) 1.04010559748387 0.00680282733923732 152.893134812456 Trimmed Mean ( 10 / 26 ) 1.04088928361667 0.00664590943165523 156.621045519939 Trimmed Mean ( 11 / 26 ) 1.04194543313793 0.00649459707526196 160.432652105043 Trimmed Mean ( 12 / 26 ) 1.04306931335714 0.00633161337687618 164.739893494849 Trimmed Mean ( 13 / 26 ) 1.04429276372222 0.00614467417022796 169.950876936975 Trimmed Mean ( 14 / 26 ) 1.04570115832692 0.00594150333920654 175.999422810485 Trimmed Mean ( 15 / 26 ) 1.04717452196 0.00569990060607613 183.718032002822 Trimmed Mean ( 16 / 26 ) 1.04877004877083 0.00539105785057195 194.538822962096 Trimmed Mean ( 17 / 26 ) 1.05034997682609 0.00506337150943691 207.440827691290 Trimmed Mean ( 18 / 26 ) 1.05196213281818 0.00468464582807249 224.555317824531 Trimmed Mean ( 19 / 26 ) 1.05372248014286 0.00417220352715794 252.557784701515 Trimmed Mean ( 20 / 26 ) 1.0553702753 0.00362444484698701 291.181220808844 Trimmed Mean ( 21 / 26 ) 1.05662395944737 0.00321684354885635 328.466070357391 Trimmed Mean ( 22 / 26 ) 1.05746275594444 0.00296819403781052 356.26469916518 Trimmed Mean ( 23 / 26 ) 1.05825005305882 0.00271734856678972 389.442144446357 Trimmed Mean ( 24 / 26 ) 1.0589205250625 0.00248580657341059 425.98669437487 Trimmed Mean ( 25 / 26 ) 1.05930410856667 0.00238447866585479 444.249774064103 Trimmed Mean ( 26 / 26 ) 1.05980702032143 0.00225735295201755 469.491055607501 Median 1.06377769 Midrange 1.0554364905 Midmean - Weighted Average at Xnp 1.05306272056098 Midmean - Weighted Average at X(n+1)p 1.0553702753 Midmean - Empirical Distribution Function 1.05306272056098 Midmean - Empirical Distribution Function - Averaging 1.0553702753 Midmean - Empirical Distribution Function - Interpolation 1.0553702753 Midmean - Closest Observation 1.05306272056098 Midmean - True Basic - Statistics Graphics Toolkit 1.0553702753 Midmean - MS Excel (old versions) 1.05372248014286 Number of observations 80

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138708ydbkc4j2j7y64qk/1bcoe1256138633.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138708ydbkc4j2j7y64qk/1bcoe1256138633.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138708ydbkc4j2j7y64qk/2d0an1256138633.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138708ydbkc4j2j7y64qk/2d0an1256138633.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')

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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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