WS3 Part2 Vraag2 C

*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: Tue, 20 Oct 2009 11:34:45 -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/20/t12560601371dazrxv2cxk1qy7.htm/, Retrieved Tue, 20 Oct 2009 19:35:37 +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/20/t12560601371dazrxv2cxk1qy7.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:

Dataseries X:

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18.54166666666670 22.54166666666670 9.44166666666668 19.24166666666670 21.84166666666670 26.54166666666670 15.54166666666670 5.94166666666668 31.94166666666670 44.94166666666670 13.44166666666670 0.54166666666667 8.54166666666667 18.94166666666670 26.74166666666670 27.84166666666670 25.04166666666670 28.94166666666670 12.64166666666670 -2.95833333333333 30.64166666666670 36.54166666666670 10.14166666666670 2.94166666666666 3.34166666666667 -4.55833333333334 14.24166666666670 12.44166666666670 5.64166666666666 29.84166666666670 -1.45833333333333 -6.05833333333332 18.14166666666670 25.64166666666670 19.24166666666670 12.54166666666670 2.34166666666667 1.14166666666666 18.04166666666670 15.84166666666670 9.34166666666667 12.54166666666670 -22.05833333333330 -28.55833333333330 -16.75833333333330 -15.35833333333330 -3.55833333333332 -29.85833333333330 -26.55833333333330 -29.85833333333330 -3.65833333333335 -46.15833333333330 -45.05833333333330 -8.55833333333332 etc...

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 2.4187943314935e-14 3.69483628962858 6.54641814113135e-15 Geometric Mean NaN Harmonic Mean 17.6511276741620 Quadratic Mean 28.3805760551512 Winsorized Mean ( 1 / 20 ) 0.110000000000024 3.57595113313805 0.0307610467549914 Winsorized Mean ( 2 / 20 ) 0.0333333333333575 3.52510871865575 0.00945597313267227 Winsorized Mean ( 3 / 20 ) 0.903333333333358 3.23135773851719 0.279552252158834 Winsorized Mean ( 4 / 20 ) 0.970000000000025 3.19099907461001 0.303980031745566 Winsorized Mean ( 5 / 20 ) 1.12000000000002 3.12091096695396 0.358869577459672 Winsorized Mean ( 6 / 20 ) 1.12000000000002 3.0763863639445 0.364063504222525 Winsorized Mean ( 7 / 20 ) 1.40000000000002 2.95533443925290 0.473719651287229 Winsorized Mean ( 8 / 20 ) 2.93333333333336 2.59017296683383 1.13248550227864 Winsorized Mean ( 9 / 20 ) 2.79833333333336 2.56957356116776 1.08902635659967 Winsorized Mean ( 10 / 20 ) 2.91500000000002 2.50818306699327 1.16219586933677 Winsorized Mean ( 11 / 20 ) 2.82333333333336 2.36383592744972 1.19438633644061 Winsorized Mean ( 12 / 20 ) 3.58333333333336 2.15830192154792 1.66025582313498 Winsorized Mean ( 13 / 20 ) 4.16833333333336 1.85300925915143 2.24949406633953 Winsorized Mean ( 14 / 20 ) 4.49500000000002 1.79104878322157 2.50970271837869 Winsorized Mean ( 15 / 20 ) 6.12000000000002 1.47574761607985 4.14705057512279 Winsorized Mean ( 16 / 20 ) 6.68000000000002 1.35033808628406 4.94690927246407 Winsorized Mean ( 17 / 20 ) 6.99166666666668 1.26659046752665 5.52006891408217 Winsorized Mean ( 18 / 20 ) 7.23166666666668 1.22081685166561 5.92362945907914 Winsorized Mean ( 19 / 20 ) 6.56666666666669 1.11442930848745 5.89240305926558 Winsorized Mean ( 20 / 20 ) 6.66666666666668 1.06969192724309 6.2323239961702 Trimmed Mean ( 1 / 20 ) 0.719252873563242 3.42440623094043 0.210037251732753 Trimmed Mean ( 2 / 20 ) 1.37202380952383 3.23447231654749 0.424187835061871 Trimmed Mean ( 3 / 20 ) 2.11574074074076 3.02881708762362 0.698536979795222 Trimmed Mean ( 4 / 20 ) 2.58205128205131 2.92213461978813 0.88361818260054 Trimmed Mean ( 5 / 20 ) 3.06566666666669 2.80263660119669 1.09385093499374 Trimmed Mean ( 6 / 20 ) 3.55208333333336 2.67476591337291 1.32799783172582 Trimmed Mean ( 7 / 20 ) 4.0807971014493 2.52278980277666 1.61757317116069 Trimmed Mean ( 8 / 20 ) 4.60303030303032 2.36316924458059 1.94782083999542 Trimmed Mean ( 9 / 20 ) 4.9011904761905 2.27256796405823 2.15667498341313 Trimmed Mean ( 10 / 20 ) 5.25166666666669 2.15580254554646 2.43606107503480 Trimmed Mean ( 11 / 20 ) 5.62061403508774 2.01525885405778 2.78902832942303 Trimmed Mean ( 12 / 20 ) 6.04444444444446 1.86485237558260 3.24124553964017 Trimmed Mean ( 13 / 20 ) 6.40637254901963 1.72485697747496 3.71414710476343 Trimmed Mean ( 14 / 20 ) 6.72916666666668 1.62931035034518 4.1300705327509 Trimmed Mean ( 15 / 20 ) 7.04833333333335 1.51085675118635 4.66512349883527 Trimmed Mean ( 16 / 20 ) 7.1809523809524 1.45497994754918 4.93543048002017 Trimmed Mean ( 17 / 20 ) 7.25320512820514 1.4120070486104 5.13680518474978 Trimmed Mean ( 18 / 20 ) 7.29166666666668 1.37118376869632 5.31778951380046 Trimmed Mean ( 19 / 20 ) 7.30075757575759 1.31785374332054 5.5398845378412 Trimmed Mean ( 20 / 20 ) 7.41666666666668 1.26827431450854 5.84784110331892 Median 8.94166666666667 Midrange -20.8583333333333 Midmean - Weighted Average at Xnp 6.32553763440862 Midmean - Weighted Average at X(n+1)p 7.04833333333335 Midmean - Empirical Distribution Function 6.32553763440862 Midmean - Empirical Distribution Function - Averaging 7.04833333333335 Midmean - Empirical Distribution Function - Interpolation 7.04833333333335 Midmean - Closest Observation 6.32553763440862 Midmean - True Basic - Statistics Graphics Toolkit 7.04833333333335 Midmean - MS Excel (old versions) 7.10833333333335 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t12560601371dazrxv2cxk1qy7/163ue1256060080.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560601371dazrxv2cxk1qy7/163ue1256060080.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560601371dazrxv2cxk1qy7/2iy3x1256060080.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560601371dazrxv2cxk1qy7/2iy3x1256060080.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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