WS 3 - Vraag 2 (2)

*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 10:21:46 -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/t1256142170w2hplcnvmn23500.htm/, Retrieved Wed, 21 Oct 2009 18:22:52 +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/t1256142170w2hplcnvmn23500.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:

SHW WS 3 - Vraag 2 (2)

Dataseries X:

» Textbox « » Textfile « » CSV «

-1 -1,3 0,5 -1,4 -0,8 -0,6 0,3 -0,1 -0,4 -0,4 -0,7 -0,8 -0,1 -1,1 0,8 -0,9 -0,9 -0,5 0,5 0 0,1 -0,4 -0,6 -0,4 0 -0,9 0,9 -0,8 -0,6 0,1 1,3 0,9 0,3 0,7 0,2 -0,4 -0,5 -0,9 1 -0,6 -0,3 -0,3 0,6 0 -0,2 -0,7 -0,2 0,1 -0,6 -0,1 0,4 -0,3 0,1 0,7 1,9 1,6 0 1,1 0,8 0,5 0,7 0,7 2,3 1,2 1,3 2,1 1,9 1,6 0,7 0,8 0,2 0,1 0,4

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.131506849315068 0.0985217356267181 1.33480037149696 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 0.84626496061319 Winsorized Mean ( 1 / 24 ) 0.13013698630137 0.0974305538790256 1.33568968994012 Winsorized Mean ( 2 / 24 ) 0.13013698630137 0.0948981054832133 1.37133387056278 Winsorized Mean ( 3 / 24 ) 0.134246575342466 0.0941843778164186 1.42535926291444 Winsorized Mean ( 4 / 24 ) 0.123287671232877 0.0892536393134169 1.38131814210901 Winsorized Mean ( 5 / 24 ) 0.123287671232877 0.0892536393134169 1.38131814210901 Winsorized Mean ( 6 / 24 ) 0.0986301369863014 0.0839586844534152 1.17474609837445 Winsorized Mean ( 7 / 24 ) 0.0986301369863014 0.0839586844534152 1.17474609837445 Winsorized Mean ( 8 / 24 ) 0.0986301369863014 0.080061172167009 1.23193471088029 Winsorized Mean ( 9 / 24 ) 0.0863013698630137 0.0777664582338018 1.10975055085513 Winsorized Mean ( 10 / 24 ) 0.0726027397260274 0.0753545721558872 0.963481546625106 Winsorized Mean ( 11 / 24 ) 0.0726027397260274 0.0704751290362858 1.03018952528127 Winsorized Mean ( 12 / 24 ) 0.0726027397260274 0.0704751290362858 1.03018952528127 Winsorized Mean ( 13 / 24 ) 0.0726027397260274 0.0649979590468889 1.11700029955791 Winsorized Mean ( 14 / 24 ) 0.0726027397260274 0.0649979590468889 1.11700029955791 Winsorized Mean ( 15 / 24 ) 0.0726027397260274 0.0649979590468889 1.11700029955791 Winsorized Mean ( 16 / 24 ) 0.0506849315068493 0.0616899033004658 0.821608217798367 Winsorized Mean ( 17 / 24 ) 0.0506849315068493 0.0616899033004658 0.821608217798367 Winsorized Mean ( 18 / 24 ) 0.0753424657534247 0.0581873849979428 1.29482474175611 Winsorized Mean ( 19 / 24 ) 0.0753424657534246 0.0581873849979428 1.29482474175611 Winsorized Mean ( 20 / 24 ) 0.102739726027397 0.0545485346126325 1.88345528907397 Winsorized Mean ( 21 / 24 ) 0.073972602739726 0.0502666935120788 1.47160271685566 Winsorized Mean ( 22 / 24 ) 0.0438356164383562 0.0459959258573118 0.95303259193744 Winsorized Mean ( 23 / 24 ) 0.0438356164383562 0.0459959258573118 0.95303259193744 Winsorized Mean ( 24 / 24 ) 0.0438356164383562 0.0459959258573118 0.95303259193744 Trimmed Mean ( 1 / 24 ) 0.122535211267606 0.0940524530030435 1.30283907920658 Trimmed Mean ( 2 / 24 ) 0.114492753623188 0.0900240415534932 1.2718019725337 Trimmed Mean ( 3 / 24 ) 0.105970149253731 0.086853656530473 1.22010003363015 Trimmed Mean ( 4 / 24 ) 0.0953846153846154 0.0833617801545321 1.14422478991926 Trimmed Mean ( 5 / 24 ) 0.0873015873015873 0.0810356689302696 1.07732296720731 Trimmed Mean ( 6 / 24 ) 0.078688524590164 0.0782009026158675 1.00623550314619 Trimmed Mean ( 7 / 24 ) 0.0745762711864407 0.0763192263800433 0.97716230527648 Trimmed Mean ( 8 / 24 ) 0.0701754385964912 0.0739998015424717 0.948319281048537 Trimmed Mean ( 9 / 24 ) 0.0654545454545455 0.0721118744485683 0.907680544363454 Trimmed Mean ( 10 / 24 ) 0.0622641509433962 0.0703106529478714 0.8855578540788 Trimmed Mean ( 11 / 24 ) 0.0607843137254902 0.0686039175336304 0.886018115447897 Trimmed Mean ( 12 / 24 ) 0.0591836734693878 0.0675065106048194 0.876710600787038 Trimmed Mean ( 13 / 24 ) 0.0574468085106383 0.0660603178564256 0.869611445641122 Trimmed Mean ( 14 / 24 ) 0.0555555555555556 0.0653317528840655 0.850360706747631 Trimmed Mean ( 15 / 24 ) 0.0534883720930233 0.0643003780552122 0.831851595757258 Trimmed Mean ( 16 / 24 ) 0.051219512195122 0.0628705552877432 0.814682039321949 Trimmed Mean ( 17 / 24 ) 0.0512820512820513 0.0616760719608573 0.831474016610484 Trimmed Mean ( 18 / 24 ) 0.0513513513513513 0.0599826828890714 0.856102943016365 Trimmed Mean ( 19 / 24 ) 0.0485714285714286 0.0584637255302906 0.830795987270145 Trimmed Mean ( 20 / 24 ) 0.0454545454545454 0.0562547824719302 0.808012109498889 Trimmed Mean ( 21 / 24 ) 0.0387096774193548 0.0540166082295083 0.716625472944975 Trimmed Mean ( 22 / 24 ) 0.0344827586206897 0.052116736641427 0.661644624028123 Trimmed Mean ( 23 / 24 ) 0.0333333333333333 0.0506369683541833 0.658280588604383 Trimmed Mean ( 24 / 24 ) 0.032 0.0482078831727758 0.663791850916018 Median 0 Midrange 0.45 Midmean - Weighted Average at Xnp 0.0846153846153846 Midmean - Weighted Average at X(n+1)p 0.0846153846153846 Midmean - Empirical Distribution Function 0.0846153846153846 Midmean - Empirical Distribution Function - Averaging 0.0846153846153846 Midmean - Empirical Distribution Function - Interpolation 0.0846153846153846 Midmean - Closest Observation 0.00681818181818177 Midmean - True Basic - Statistics Graphics Toolkit 0.0846153846153846 Midmean - MS Excel (old versions) 0.0846153846153846 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142170w2hplcnvmn23500/1bidk1256142103.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142170w2hplcnvmn23500/1bidk1256142103.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142170w2hplcnvmn23500/29ub71256142103.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142170w2hplcnvmn23500/29ub71256142103.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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