TIJDREEKS B - STAP 9

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 29 Jul 2010 11:55:58 +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/Jul/29/t1280404577ljffomu3ztwbwef.htm/, Retrieved Thu, 29 Jul 2010 13:56:20 +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/Jul/29/t1280404577ljffomu3ztwbwef.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:

Hoes Isabelle

Dataseries X:

» Textbox « » Textfile « » CSV «

158 157 156 154 152 151 152 154 155 155 156 158 156 152 145 141 140 145 143 141 144 139 141 142 141 132 122 122 127 128 122 123 128 128 128 129 124 121 109 110 107 107 104 110 114 118 117 122 113 106 102 111 106 110 105 104 106 110 107 111 101 105 108 124 122 128 124 121 125 134 126 126 111 117 118 128 127 129 124 113 120 127 114 107

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 126.785714285714 1.84279398771910 68.8008074318941 Geometric Mean 125.700048318972 Harmonic Mean 124.645379529474 Quadratic Mean 127.89243992698 Winsorized Mean ( 1 / 28 ) 126.797619047619 1.84082439951566 68.8808878679469 Winsorized Mean ( 2 / 28 ) 126.821428571429 1.82858044900601 69.3551266176815 Winsorized Mean ( 3 / 28 ) 126.785714285714 1.82157902700567 69.6020937911907 Winsorized Mean ( 4 / 28 ) 126.833333333333 1.81453882763885 69.898384868608 Winsorized Mean ( 5 / 28 ) 126.833333333333 1.81453882763885 69.898384868608 Winsorized Mean ( 6 / 28 ) 126.833333333333 1.79066820969590 70.830169791685 Winsorized Mean ( 7 / 28 ) 126.833333333333 1.79066820969590 70.830169791685 Winsorized Mean ( 8 / 28 ) 126.738095238095 1.77282015248683 71.4895388910789 Winsorized Mean ( 9 / 28 ) 126.845238095238 1.7579826987599 72.153860322241 Winsorized Mean ( 10 / 28 ) 126.607142857143 1.71457404584215 73.8417469715967 Winsorized Mean ( 11 / 28 ) 126.607142857143 1.71457404584215 73.8417469715967 Winsorized Mean ( 12 / 28 ) 126.607142857143 1.71457404584215 73.8417469715967 Winsorized Mean ( 13 / 28 ) 126.607142857143 1.66603698866581 75.9929963851112 Winsorized Mean ( 14 / 28 ) 125.773809523810 1.47617833078490 85.2023139080591 Winsorized Mean ( 15 / 28 ) 125.952380952381 1.45213404219700 86.7360569288921 Winsorized Mean ( 16 / 28 ) 125.761904761905 1.42236652086731 88.4173684608517 Winsorized Mean ( 17 / 28 ) 125.559523809524 1.39144909239565 90.236519967359 Winsorized Mean ( 18 / 28 ) 125.345238095238 1.35945025839647 92.2028866602947 Winsorized Mean ( 19 / 28 ) 125.345238095238 1.29581767410636 96.7306131101205 Winsorized Mean ( 20 / 28 ) 125.345238095238 1.29581767410636 96.7306131101205 Winsorized Mean ( 21 / 28 ) 125.345238095238 1.29581767410636 96.7306131101205 Winsorized Mean ( 22 / 28 ) 125.869047619048 1.22776024824359 102.519240054492 Winsorized Mean ( 23 / 28 ) 125.595238095238 1.18741718286194 105.771787631139 Winsorized Mean ( 24 / 28 ) 125.595238095238 1.10948539647234 113.201344059664 Winsorized Mean ( 25 / 28 ) 124.107142857143 0.901808258211873 137.620321977563 Winsorized Mean ( 26 / 28 ) 124.416666666667 0.69775649273891 178.309579289320 Winsorized Mean ( 27 / 28 ) 123.452380952381 0.578195493957344 213.513218699502 Winsorized Mean ( 28 / 28 ) 123.785714285714 0.534004730665147 231.806400163401 Trimmed Mean ( 1 / 28 ) 126.719512195122 1.82147138922182 69.5698614564898 Trimmed Mean ( 2 / 28 ) 126.6375 1.79866720611525 70.4062983799605 Trimmed Mean ( 3 / 28 ) 126.538461538462 1.77915673954271 71.1227171423836 Trimmed Mean ( 4 / 28 ) 126.447368421053 1.75892658024189 71.8889405853786 Trimmed Mean ( 5 / 28 ) 126.337837837838 1.73709629186817 72.7293233134284 Trimmed Mean ( 6 / 28 ) 126.222222222222 1.71094038129616 73.7735946863325 Trimmed Mean ( 7 / 28 ) 126.1 1.68578885331794 74.8017758877763 Trimmed Mean ( 8 / 28 ) 125.970588235294 1.65546035445670 76.093992765315 Trimmed Mean ( 9 / 28 ) 125.848484848485 1.62300513009894 77.5404110033917 Trimmed Mean ( 10 / 28 ) 125.703125 1.58672564033247 79.2217140788505 Trimmed Mean ( 11 / 28 ) 125.580645161290 1.55194703577447 80.9181255973865 Trimmed Mean ( 12 / 28 ) 125.45 1.50937278850828 83.1139934117818 Trimmed Mean ( 13 / 28 ) 125.310344827586 1.45702854530101 86.0040424271154 Trimmed Mean ( 14 / 28 ) 125.160714285714 1.40240442545713 89.2472328336504 Trimmed Mean ( 15 / 28 ) 125.092592592593 1.37392827644603 91.0473965323516 Trimmed Mean ( 16 / 28 ) 125 1.34225896353444 93.12658987268 Trimmed Mean ( 17 / 28 ) 124.92 1.30800986078789 95.5038671686718 Trimmed Mean ( 18 / 28 ) 124.854166666667 1.27057170891457 98.2661315301343 Trimmed Mean ( 19 / 28 ) 124.804347826087 1.22912307816298 101.539341375492 Trimmed Mean ( 20 / 28 ) 124.75 1.18888661116491 104.930107571626 Trimmed Mean ( 21 / 28 ) 124.690476190476 1.13567843146544 109.793822560828 Trimmed Mean ( 22 / 28 ) 124.625 1.06439310985542 117.085500503595 Trimmed Mean ( 23 / 28 ) 124.5 0.98477022902956 126.425430349056 Trimmed Mean ( 24 / 28 ) 124.388888888889 0.886653936336985 140.290234770483 Trimmed Mean ( 25 / 28 ) 124.264705882353 0.77195589671272 160.973841137193 Trimmed Mean ( 26 / 28 ) 124.28125 0.687202098214435 180.851092164767 Trimmed Mean ( 27 / 28 ) 124.266666666667 0.639564027751616 194.299024451900 Trimmed Mean ( 28 / 28 ) 124.357142857143 0.609046191839672 204.183433905912 Median 124 Midrange 129.5 Midmean - Weighted Average at Xnp 124.804347826087 Midmean - Weighted Average at X(n+1)p 124.804347826087 Midmean - Empirical Distribution Function 124.804347826087 Midmean - Empirical Distribution Function - Averaging 124.804347826087 Midmean - Empirical Distribution Function - Interpolation 124.804347826087 Midmean - Closest Observation 124.804347826087 Midmean - True Basic - Statistics Graphics Toolkit 124.804347826087 Midmean - MS Excel (old versions) 124.804347826087 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/29/t1280404577ljffomu3ztwbwef/188ym1280404557.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280404577ljffomu3ztwbwef/188ym1280404557.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280404577ljffomu3ztwbwef/2jhfp1280404557.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280404577ljffomu3ztwbwef/2jhfp1280404557.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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