*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 11:51:36 -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/t1256061157yr9m9r3ftcdp7u4.htm/, Retrieved Tue, 20 Oct 2009 19:52:38 +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/t1256061157yr9m9r3ftcdp7u4.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:

ws3oefening3.1

Dataseries X:

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0,720720721 0,743119266 0,77 0,815217391 0,826086957 0,821052632 0,8125 0,821052632 0,824175824 0,842696629 0,788888889 0,742574257 0,72815534 0,745098039 0,802083333 0,836956522 0,849462366 0,861702128 0,872340426 0,891304348 0,911111111 0,877777778 0,811111111 0,704081633 0,66 0,683673469 0,741935484 0,777777778 0,788888889 0,791208791 0,78021978 0,758241758 0,760869565 0,772727273 0,771084337 0,797619048 0,814814815 0,831168831 0,797468354 0,784810127 0,8125 0,860759494 0,894736842 0,901408451 0,897058824 0,892307692 0,884057971 0,87804878 0,83908046 0,831325301 0,772151899 0,773333333 0,794871795 0,855421687 0,916666667 0,963414634 1 1,027777778 1,02739726 0,987654321

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 0.825695847016667 0.010084018365634 81.881628640286 Geometric Mean 0.822157833190205 Harmonic Mean 0.818703314041358 Quadratic Mean 0.82932092095767 Winsorized Mean ( 1 / 20 ) 0.826084062866667 0.009979159669146 82.7809244721065 Winsorized Mean ( 2 / 20 ) 0.825851093 0.00952501785460792 86.7033642987323 Winsorized Mean ( 3 / 20 ) 0.82606576345 0.00916574100752813 90.1253660529492 Winsorized Mean ( 4 / 20 ) 0.824945425583333 0.00860780497750503 95.8369093792415 Winsorized Mean ( 5 / 20 ) 0.822198107 0.00743423046569785 110.596262894147 Winsorized Mean ( 6 / 20 ) 0.8217064287 0.00730505473458315 112.484636810444 Winsorized Mean ( 7 / 20 ) 0.820638036083333 0.00706611729777163 116.137052570884 Winsorized Mean ( 8 / 20 ) 0.820321922216667 0.00690642702910275 118.776600224681 Winsorized Mean ( 9 / 20 ) 0.821945182766667 0.00649411951141255 126.567609561575 Winsorized Mean ( 10 / 20 ) 0.821978292266667 0.00634546981643262 129.537814542593 Winsorized Mean ( 11 / 20 ) 0.82346825895 0.00604843064635367 136.145771870003 Winsorized Mean ( 12 / 20 ) 0.82223585095 0.0057457843245452 143.102456428363 Winsorized Mean ( 13 / 20 ) 0.821165164666667 0.00547738918346328 149.919083191283 Winsorized Mean ( 14 / 20 ) 0.8212361848 0.00544594500195784 150.797737491797 Winsorized Mean ( 15 / 20 ) 0.8200283618 0.00518708788502892 158.090315794877 Winsorized Mean ( 16 / 20 ) 0.818376667666667 0.00453363206331674 180.512369825608 Winsorized Mean ( 17 / 20 ) 0.8188014886 0.00438625121564737 186.674553814664 Winsorized Mean ( 18 / 20 ) 0.8185772506 0.00392577584427338 208.513497222231 Winsorized Mean ( 19 / 20 ) 0.81798174025 0.00344241569254855 237.618525275899 Winsorized Mean ( 20 / 20 ) 0.815726494583333 0.00310096348788543 263.055820479713 Trimmed Mean ( 1 / 20 ) 0.82506850074138 0.00939260051383524 87.8423924797034 Trimmed Mean ( 2 / 20 ) 0.823980398464286 0.00865392821013448 95.2146098807863 Trimmed Mean ( 3 / 20 ) 0.822941123722222 0.0080452450294196 102.289131121913 Trimmed Mean ( 4 / 20 ) 0.821739339211539 0.00746007897940506 110.151560255609 Trimmed Mean ( 5 / 20 ) 0.8207775133 0.00696097162890053 117.911342993024 Trimmed Mean ( 6 / 20 ) 0.820422364875 0.00676669884473857 121.244107902470 Trimmed Mean ( 7 / 20 ) 0.820143220565217 0.0065574329304608 125.070775296147 Trimmed Mean ( 8 / 20 ) 0.820046827931818 0.006357592390429 128.987009165034 Trimmed Mean ( 9 / 20 ) 0.819997703952381 0.00614027101266616 133.544220159157 Trimmed Mean ( 10 / 20 ) 0.81967312415 0.0059657404652056 137.396711930503 Trimmed Mean ( 11 / 20 ) 0.819309150236842 0.00576827415653232 142.037137626167 Trimmed Mean ( 12 / 20 ) 0.81867898225 0.00557437608042804 146.864684125714 Trimmed Mean ( 13 / 20 ) 0.81815591332353 0.00539061190264599 151.774219346404 Trimmed Mean ( 14 / 20 ) 0.8177218866875 0.0052068411047741 157.047597618782 Trimmed Mean ( 15 / 20 ) 0.8172198441 0.00494283621767329 165.334194399968 Trimmed Mean ( 16 / 20 ) 0.816818627285714 0.00464147199549077 175.982668446403 Trimmed Mean ( 17 / 20 ) 0.816593909923077 0.00442834867518606 184.401448444835 Trimmed Mean ( 18 / 20 ) 0.816269266 0.00414205875439104 197.068490429950 Trimmed Mean ( 19 / 20 ) 0.815919571363636 0.00387722604790591 210.438999759716 Trimmed Mean ( 20 / 20 ) 0.81559396575 0.00365890915671564 222.906317379605 Median 0.815016103 Midrange 0.843888889 Midmean - Weighted Average at Xnp 0.815784599870968 Midmean - Weighted Average at X(n+1)p 0.8172198441 Midmean - Empirical Distribution Function 0.815784599870968 Midmean - Empirical Distribution Function - Averaging 0.8172198441 Midmean - Empirical Distribution Function - Interpolation 0.8172198441 Midmean - Closest Observation 0.815784599870968 Midmean - True Basic - Statistics Graphics Toolkit 0.8172198441 Midmean - MS Excel (old versions) 0.8177218866875 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061157yr9m9r3ftcdp7u4/132ew1256061091.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061157yr9m9r3ftcdp7u4/132ew1256061091.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061157yr9m9r3ftcdp7u4/2fvws1256061091.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061157yr9m9r3ftcdp7u4/2fvws1256061091.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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