Central Tendency - Invoer/uitvoer

*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 15:48:50 -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/t1256075484f1cqkc20y936o30.htm/, Retrieved Tue, 20 Oct 2009 23:51:24 +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/t1256075484f1cqkc20y936o30.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)

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Dataseries X:

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1,038351422 0,933031106 0,932783124 0,953755367 1,009865664 0,979532493 0,98651077 0,964661281 0,946761816 0,959068881 0,985710058 0,92582159 1,036865325 0,944443576 0,944901812 0,989151445 1,054361624 1,033478919 1,001368875 1,019812646 0,993902155 0,961444482 0,957449711 0,93308639 1,045170549 0,953166261 0,966782226 0,972992606 1,013607482 0,984839518 0,973220775 0,957284573 0,972067159 0,986878944 0,954654488 0,978986976 1,003056035 0,970081156 0,991376354 1,022609041 1,089901216 1,060373568 0,985952627 1,037512164 1,025335152 1,006376649 1,018762056 1,01601847 1,112410461 1,037903689 1,045436015 1,09935434 1,101920787 1,080574973 1,024388761 1,024282249 0,993865289 0,984935203 1,005791114 0,94742834

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.9988569633 0.00582949424588891 171.345389697299 Geometric Mean 0.997869402797325 Harmonic Mean 0.996897702888162 Quadratic Mean 0.9998601053745 Winsorized Mean ( 1 / 20 ) 0.998798160966667 0.00575043513794848 173.690883734234 Winsorized Mean ( 2 / 20 ) 0.9987208788 0.0057230771298786 174.507674129701 Winsorized Mean ( 3 / 20 ) 0.9982509868 0.00558632912452421 178.695340812921 Winsorized Mean ( 4 / 20 ) 0.998386383 0.00527699106106421 189.196148230476 Winsorized Mean ( 5 / 20 ) 0.996741118916667 0.00485977875758573 205.100102007902 Winsorized Mean ( 6 / 20 ) 0.996325924916667 0.00469659494315788 212.137929068833 Winsorized Mean ( 7 / 20 ) 0.995362365 0.00447453081197623 222.4506673048 Winsorized Mean ( 8 / 20 ) 0.996092025666667 0.00433402337140294 229.830792385466 Winsorized Mean ( 9 / 20 ) 0.995157522516667 0.00413010329090341 240.952211705821 Winsorized Mean ( 10 / 20 ) 0.99523275385 0.00409156835651126 243.239918567217 Winsorized Mean ( 11 / 20 ) 0.995643156516667 0.00399912019106296 248.965549658068 Winsorized Mean ( 12 / 20 ) 0.995546816316667 0.00397086389010152 250.712903758384 Winsorized Mean ( 13 / 20 ) 0.995163915183333 0.00378632897415096 262.830811051353 Winsorized Mean ( 14 / 20 ) 0.993818009783333 0.00338288924694851 293.777873656312 Winsorized Mean ( 15 / 20 ) 0.994385611783333 0.00321726748702955 309.077692729066 Winsorized Mean ( 16 / 20 ) 0.994922793916667 0.00312530451115895 318.344273450564 Winsorized Mean ( 17 / 20 ) 0.99538341515 0.00290967329269358 342.094563554433 Winsorized Mean ( 18 / 20 ) 0.99514029755 0.00269067896825486 369.84727992111 Winsorized Mean ( 19 / 20 ) 0.995100668933333 0.00259668865260849 383.219092490626 Winsorized Mean ( 20 / 20 ) 0.9942621966 0.00244605244586715 406.476238185287 Trimmed Mean ( 1 / 20 ) 0.998158374948276 0.00555571688016638 179.663290350818 Trimmed Mean ( 2 / 20 ) 0.997472889928571 0.00531403702588887 187.705295440941 Trimmed Mean ( 3 / 20 ) 0.996779562777778 0.00503022160664233 198.158180836714 Trimmed Mean ( 4 / 20 ) 0.996213630461538 0.00474351344397562 210.015981239972 Trimmed Mean ( 5 / 20 ) 0.9955618047 0.00451094907415163 220.698967852399 Trimmed Mean ( 6 / 20 ) 0.995266976145833 0.00437002244342438 227.748710454204 Trimmed Mean ( 7 / 20 ) 0.995036769891304 0.0042412560346736 234.608984168031 Trimmed Mean ( 8 / 20 ) 0.994973342272727 0.00414004701161898 240.328996139500 Trimmed Mean ( 9 / 20 ) 0.994773577380952 0.00404386459866863 245.995767936559 Trimmed Mean ( 10 / 20 ) 0.994709586525 0.00396926542475555 250.602940363017 Trimmed Mean ( 11 / 20 ) 0.994626981157895 0.00387459036461241 256.705067519413 Trimmed Mean ( 12 / 20 ) 0.994473015194444 0.003766293453998 264.045546992306 Trimmed Mean ( 13 / 20 ) 0.994315103264706 0.00362015264776617 274.661098580539 Trimmed Mean ( 14 / 20 ) 0.99419267846875 0.00346756232489685 286.712273729160 Trimmed Mean ( 15 / 20 ) 0.994246202566667 0.00337083716788021 294.955274624526 Trimmed Mean ( 16 / 20 ) 0.994226286964286 0.00327358355735258 303.711901512708 Trimmed Mean ( 17 / 20 ) 0.99412582923077 0.00314881182824524 315.714588059323 Trimmed Mean ( 18 / 20 ) 0.993940890125 0.00302600439412739 328.466439789035 Trimmed Mean ( 19 / 20 ) 0.993759161727273 0.0029076572335137 341.773146529512 Trimmed Mean ( 20 / 20 ) 0.9935473448 0.00273797539706403 362.87665180096 Median 0.9902638995 Midrange 1.0191160255 Midmean - Weighted Average at Xnp 0.993188082548387 Midmean - Weighted Average at X(n+1)p 0.994246202566667 Midmean - Empirical Distribution Function 0.993188082548387 Midmean - Empirical Distribution Function - Averaging 0.994246202566667 Midmean - Empirical Distribution Function - Interpolation 0.994246202566667 Midmean - Closest Observation 0.993188082548387 Midmean - True Basic - Statistics Graphics Toolkit 0.994246202566667 Midmean - MS Excel (old versions) 0.99419267846875 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256075484f1cqkc20y936o30/1f3zx1256075325.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256075484f1cqkc20y936o30/1f3zx1256075325.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256075484f1cqkc20y936o30/264st1256075325.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256075484f1cqkc20y936o30/264st1256075325.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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