opgave 5, oef. 2 - Sandy Dorekens

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 08 Nov 2008 03:52:45 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/08/t1226141733ejnslk1hwswor55.htm/, Retrieved Sat, 08 Nov 2008 10:55:33 +0000

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/2008/Nov/08/t1226141733ejnslk1hwswor55.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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9.026 9.787 9.536 9.490 9.736 9.694 9.647 9.753 10.070 10.137 9.984 9.732 9.103 9.155 9.308 9.394 9.948 10.177 10.002 9.728 10.002 10.063 10.018 9.960 10.236 10.893 10.756 10.940 10.997 10.827 10.166 10.186 10.457 10.368 10.244 10.511 10.812 10.738 10.171 9.721 9.897 9.828 9.924 10.371 10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 11.1306190476190 0.212329673836461 52.4214013355099 Geometric Mean 10.9864933521148 Harmonic Mean 10.8636414921880 Quadratic Mean 11.2974618072253 Winsorized Mean ( 1 / 28 ) 11.1194642857143 0.208466640847111 53.3392980312342 Winsorized Mean ( 2 / 28 ) 11.1196309523810 0.208019815809203 53.4546716577229 Winsorized Mean ( 3 / 28 ) 11.1191666666667 0.205760975712179 54.0392395991565 Winsorized Mean ( 4 / 28 ) 11.1141666666667 0.202852938454217 54.7892810987063 Winsorized Mean ( 5 / 28 ) 11.0994642857143 0.196901842947928 56.3705454430389 Winsorized Mean ( 6 / 28 ) 11.0929642857143 0.194084275014555 57.1553995545614 Winsorized Mean ( 7 / 28 ) 11.0996309523810 0.192563767578385 57.6413262576136 Winsorized Mean ( 8 / 28 ) 11.0866785714286 0.187796453848925 59.0356119309228 Winsorized Mean ( 9 / 28 ) 11.0871071428571 0.186928881596877 59.3119000560176 Winsorized Mean ( 10 / 28 ) 11.0825833333333 0.185530330410161 59.7346175627053 Winsorized Mean ( 11 / 28 ) 11.0383214285714 0.174530279500796 63.2458818042578 Winsorized Mean ( 12 / 28 ) 10.9343214285714 0.149670317714618 73.0560447491019 Winsorized Mean ( 13 / 28 ) 10.8160833333333 0.122120479115861 88.568955933031 Winsorized Mean ( 14 / 28 ) 10.7455833333333 0.105190006768253 102.15403215067 Winsorized Mean ( 15 / 28 ) 10.6439761904762 0.0823189785013875 129.301606801362 Winsorized Mean ( 16 / 28 ) 10.5594047619048 0.0627584252698747 168.254775617729 Winsorized Mean ( 17 / 28 ) 10.5450357142857 0.0587197180815308 179.582533070820 Winsorized Mean ( 18 / 28 ) 10.5486785714286 0.0578212251632455 182.436095770138 Winsorized Mean ( 19 / 28 ) 10.4724523809524 0.0452733439839723 231.316078279083 Winsorized Mean ( 20 / 28 ) 10.4645952380952 0.0426357139917559 245.44200761171 Winsorized Mean ( 21 / 28 ) 10.4573452380952 0.0404732634315077 258.376625739411 Winsorized Mean ( 22 / 28 ) 10.4518452380952 0.0397665032803513 262.830381751456 Winsorized Mean ( 23 / 28 ) 10.4562261904762 0.0391726958574861 266.926387413236 Winsorized Mean ( 24 / 28 ) 10.4616547619048 0.0365137156778265 286.513014841099 Winsorized Mean ( 25 / 28 ) 10.4580833333333 0.0355272361978377 294.368052586366 Winsorized Mean ( 26 / 28 ) 10.4741785714286 0.0322713420588173 324.565943131169 Winsorized Mean ( 27 / 28 ) 10.48125 0.0308258571590906 340.014876014861 Winsorized Mean ( 28 / 28 ) 10.4665833333333 0.028588536514855 366.111197328857 Trimmed Mean ( 1 / 28 ) 11.0839268292683 0.203297003715029 54.5208568091105 Trimmed Mean ( 2 / 28 ) 11.0466125 0.197217325744904 56.012383588897 Trimmed Mean ( 3 / 28 ) 11.0072948717949 0.190312305424694 57.8380617439917 Trimmed Mean ( 4 / 28 ) 10.9660789473684 0.183134439892643 59.879938223509 Trimmed Mean ( 5 / 28 ) 10.9240540540541 0.175638341659925 62.1962946746871 Trimmed Mean ( 6 / 28 ) 10.883125 0.168577979543045 64.5584021679479 Trimmed Mean ( 7 / 28 ) 10.8411571428571 0.160857794579250 67.395908113834 Trimmed Mean ( 8 / 28 ) 10.7955441176471 0.151778747400108 71.1268494606077 Trimmed Mean ( 9 / 28 ) 10.7492272727273 0.141839287884650 75.7845547100396 Trimmed Mean ( 10 / 28 ) 10.699953125 0.129490763578054 82.6310142078227 Trimmed Mean ( 11 / 28 ) 10.6481129032258 0.113794351666038 93.573299090237 Trimmed Mean ( 12 / 28 ) 10.59845 0.0962701572553307 110.090710373418 Trimmed Mean ( 13 / 28 ) 10.5579137931034 0.0809099986361384 130.489605377249 Trimmed Mean ( 14 / 28 ) 10.528125 0.0693868230243724 151.730898477683 Trimmed Mean ( 15 / 28 ) 10.5039629629630 0.0592945952909862 177.148741996047 Trimmed Mean ( 16 / 28 ) 10.4888846153846 0.0530442176872267 197.738510863370 Trimmed Mean ( 17 / 28 ) 10.48148 0.0502368613344295 208.641219247839 Trimmed Mean ( 18 / 28 ) 10.4749375 0.0475964065171122 220.078326632368 Trimmed Mean ( 19 / 28 ) 10.4674565217391 0.0443514478250214 236.011608077286 Trimmed Mean ( 20 / 28 ) 10.4669545454545 0.0432179191477367 242.190155191743 Trimmed Mean ( 21 / 28 ) 10.4671904761905 0.0422703295981739 247.625002589113 Trimmed Mean ( 22 / 28 ) 10.468175 0.0414410438114134 252.604037862505 Trimmed Mean ( 23 / 28 ) 10.4698157894737 0.0404331606098694 258.941315285605 Trimmed Mean ( 24 / 28 ) 10.4711944444444 0.0391641603948767 267.366754166757 Trimmed Mean ( 25 / 28 ) 10.4721764705882 0.0380623953118747 275.131829848899 Trimmed Mean ( 26 / 28 ) 10.47365625 0.0367228232126516 285.208361823109 Trimmed Mean ( 27 / 28 ) 10.4736 0.0357186193758233 293.225219312066 Trimmed Mean ( 28 / 28 ) 10.47275 0.0346085297388929 302.606036113426 Median 10.46 Midrange 13.045 Midmean - Weighted Average at Xnp 10.4559534883721 Midmean - Weighted Average at X(n+1)p 10.4671904761905 Midmean - Empirical Distribution Function 10.4559534883721 Midmean - Empirical Distribution Function - Averaging 10.4671904761905 Midmean - Empirical Distribution Function - Interpolation 10.4671904761905 Midmean - Closest Observation 10.4559534883721 Midmean - True Basic - Statistics Graphics Toolkit 10.4671904761905 Midmean - MS Excel (old versions) 10.4669545454545 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226141733ejnslk1hwswor55/136kv1226141559.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226141733ejnslk1hwswor55/136kv1226141559.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226141733ejnslk1hwswor55/2opyn1226141559.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226141733ejnslk1hwswor55/2opyn1226141559.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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