Central Tendency part 2.3

*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 11:37:11 -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/t1256060278yh271scjo4w59u4.htm/, Retrieved Tue, 20 Oct 2009 19:38:01 +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/t1256060278yh271scjo4w59u4.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:

Gemiddelden

Dataseries X:

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0,806451613 0,819277108 0,8125 0,776470588 0,730769231 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

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.81056377052459 0.00775112424751829 104.573703715833 Geometric Mean 0.808326844206217 Harmonic Mean 0.806073591386973 Quadratic Mean 0.812784363600253 Winsorized Mean ( 1 / 20 ) 0.810185500065574 0.00741453937543357 109.26983579721 Winsorized Mean ( 2 / 20 ) 0.810672470819672 0.00719358454090267 112.693812967679 Winsorized Mean ( 3 / 20 ) 0.81101360662295 0.00689526954798759 117.618840130717 Winsorized Mean ( 4 / 20 ) 0.811215901180328 0.00673041004098568 120.529937439224 Winsorized Mean ( 5 / 20 ) 0.811239828147541 0.00664660088507875 122.053338567196 Winsorized Mean ( 6 / 20 ) 0.812099215327869 0.00638498094455527 127.188980261621 Winsorized Mean ( 7 / 20 ) 0.812057379311475 0.00634754962738783 127.932419119290 Winsorized Mean ( 8 / 20 ) 0.811178511377049 0.00614149764402295 132.081547269909 Winsorized Mean ( 9 / 20 ) 0.810583859540984 0.00591560295631463 137.024723519641 Winsorized Mean ( 10 / 20 ) 0.812694141016393 0.0055307338474352 146.941466256466 Winsorized Mean ( 11 / 20 ) 0.812187501754098 0.00526375144212342 154.298224504776 Winsorized Mean ( 12 / 20 ) 0.811890872967213 0.00459143553482176 176.827239936133 Winsorized Mean ( 13 / 20 ) 0.811921071967213 0.0045202171502648 179.619926427572 Winsorized Mean ( 14 / 20 ) 0.810941015737705 0.00426636038087593 190.077945448014 Winsorized Mean ( 15 / 20 ) 0.809617094344262 0.00399547781446936 202.633359998218 Winsorized Mean ( 16 / 20 ) 0.808001441360656 0.00368368996288107 219.345669560287 Winsorized Mean ( 17 / 20 ) 0.80786797352459 0.00339114378421786 238.228758475046 Winsorized Mean ( 18 / 20 ) 0.807626965918033 0.00323631213448954 249.551629248339 Winsorized Mean ( 19 / 20 ) 0.806633602622951 0.00286028970211594 282.011155033083 Winsorized Mean ( 20 / 20 ) 0.808087332786885 0.00262563646063709 307.768171603927 Trimmed Mean ( 1 / 20 ) 0.810525006237288 0.00712786304859417 113.712202480819 Trimmed Mean ( 2 / 20 ) 0.810888337403509 0.00677453583659811 119.696516036249 Trimmed Mean ( 3 / 20 ) 0.811008045236364 0.00648857206427615 124.990219296707 Trimmed Mean ( 4 / 20 ) 0.811005911622642 0.00628073345685371 129.125987783743 Trimmed Mean ( 5 / 20 ) 0.810943120627451 0.00608592393071557 133.248974167198 Trimmed Mean ( 6 / 20 ) 0.810869246510204 0.00586840493194659 138.175408124271 Trimmed Mean ( 7 / 20 ) 0.810603189425532 0.00567429163677714 142.85539787411 Trimmed Mean ( 8 / 20 ) 0.8103215844 0.00543403968347083 149.119555910646 Trimmed Mean ( 9 / 20 ) 0.810169629325581 0.00518285783101277 156.317162411393 Trimmed Mean ( 10 / 20 ) 0.810101152243902 0.00491827827847069 164.712345738964 Trimmed Mean ( 11 / 20 ) 0.809695582205128 0.00467534225640072 173.184237174642 Trimmed Mean ( 12 / 20 ) 0.809322100405405 0.00442498888526491 182.898109213432 Trimmed Mean ( 13 / 20 ) 0.808949016771429 0.00427878241019481 189.060564249304 Trimmed Mean ( 14 / 20 ) 0.808526416848485 0.00408973005722191 197.696768621865 Trimmed Mean ( 15 / 20 ) 0.808187037741935 0.00389881419177223 207.290472946229 Trimmed Mean ( 16 / 20 ) 0.807986501068966 0.00370967407626305 217.805253091908 Trimmed Mean ( 17 / 20 ) 0.807984391444444 0.00353429482651139 228.61261753932 Trimmed Mean ( 18 / 20 ) 0.80800110084 0.00336866891543496 239.857677059864 Trimmed Mean ( 19 / 20 ) 0.808056227 0.0031612846379668 255.610082463092 Trimmed Mean ( 20 / 20 ) 0.808273720952381 0.00298388993560933 270.879200772976 Median 0.8125 Midrange 0.811707317 Midmean - Weighted Average at Xnp 0.806811193466667 Midmean - Weighted Average at X(n+1)p 0.808187037741936 Midmean - Empirical Distribution Function 0.808187037741936 Midmean - Empirical Distribution Function - Averaging 0.808187037741936 Midmean - Empirical Distribution Function - Interpolation 0.808187037741936 Midmean - Closest Observation 0.80706093965625 Midmean - True Basic - Statistics Graphics Toolkit 0.808187037741936 Midmean - MS Excel (old versions) 0.808187037741936 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256060278yh271scjo4w59u4/1q4lz1256060229.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256060278yh271scjo4w59u4/1q4lz1256060229.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256060278yh271scjo4w59u4/24mmp1256060229.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256060278yh271scjo4w59u4/24mmp1256060229.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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