*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 27 Oct 2009 05:47:31 -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/27/t1256644198retfe9lfrjafdzb.htm/, Retrieved Tue, 27 Oct 2009 12:50:00 +0100

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/27/t1256644198retfe9lfrjafdzb.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

2,14 2,45 2,52 2,3 2,25 2,06 1,99 2,25 2,26 2,36 2,3 2,19 2,31 2,21 2,21 2,26 2,18 2,21 2,33 2,12 2,08 1,97 2,09 2,11 2,24 2,45 2,68 2,73 2,76 2,83 3,16 3,22 3,22 3,34 3,35 3,42 3,58 3,71 3,68 3,83 3,94 3,88 4,03 4,15 4,32 4,4 4,37 4,14 4,11 4,16 3,98 4,13 3,76 3,66 3,85 4,03 4,31 4,58 4,46 4,41 3,84 2,84 2,66 2,17 1,43 1,47 1,29 1,23 1,09 0,94 0,76 0,67

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.86680555555556 0.121293050758564 23.6353652383761 Geometric Mean 2.65112009545915 Harmonic Mean 2.3875895524265 Quadratic Mean 3.04353846515678 Winsorized Mean ( 1 / 24 ) 2.86638888888889 0.120659103068068 23.7560931252062 Winsorized Mean ( 2 / 24 ) 2.87 0.119218569412004 24.073430960924 Winsorized Mean ( 3 / 24 ) 2.87583333333333 0.117762417982996 24.4206376073951 Winsorized Mean ( 4 / 24 ) 2.88194444444444 0.11584766839539 24.8770172448212 Winsorized Mean ( 5 / 24 ) 2.88263888888889 0.114399328237005 25.1980403496498 Winsorized Mean ( 6 / 24 ) 2.89347222222222 0.112033620268692 25.8268206925989 Winsorized Mean ( 7 / 24 ) 2.88277777777778 0.108814968042269 26.4924746075188 Winsorized Mean ( 8 / 24 ) 2.93722222222222 0.0996967668174774 29.4615594465528 Winsorized Mean ( 9 / 24 ) 2.93847222222222 0.0991437638211566 29.6384977629342 Winsorized Mean ( 10 / 24 ) 2.94680555555556 0.0976295388395612 30.1835447609577 Winsorized Mean ( 11 / 24 ) 2.94680555555556 0.0967216587931085 30.4668632892131 Winsorized Mean ( 12 / 24 ) 2.93513888888889 0.0942912763660067 31.1284246221854 Winsorized Mean ( 13 / 24 ) 2.93875 0.0938387425579187 31.3170223715025 Winsorized Mean ( 14 / 24 ) 2.93097222222222 0.0920202654506499 31.8513776054481 Winsorized Mean ( 15 / 24 ) 2.92680555555556 0.0901771483821268 32.4561777353302 Winsorized Mean ( 16 / 24 ) 2.92013888888889 0.0872758683319556 33.4587205455474 Winsorized Mean ( 17 / 24 ) 2.91541666666667 0.0858992152237513 33.9399685907788 Winsorized Mean ( 18 / 24 ) 2.91541666666667 0.0852160417269286 34.2120639211218 Winsorized Mean ( 19 / 24 ) 2.91805555555556 0.0841840703637462 34.6627995409 Winsorized Mean ( 20 / 24 ) 2.89861111111111 0.081248403272033 35.6759147795937 Winsorized Mean ( 21 / 24 ) 2.88402777777778 0.0790867918581183 36.4666173708465 Winsorized Mean ( 22 / 24 ) 2.88402777777778 0.0766494825919953 37.6261871607071 Winsorized Mean ( 23 / 24 ) 2.88083333333333 0.0753395417899558 38.2379991288638 Winsorized Mean ( 24 / 24 ) 2.85416666666667 0.0714897778787853 39.9241227397021 Trimmed Mean ( 1 / 24 ) 2.87371428571429 0.118167017189627 24.3190896585189 Trimmed Mean ( 2 / 24 ) 2.88147058823529 0.11519275457692 25.0143387821427 Trimmed Mean ( 3 / 24 ) 2.88772727272727 0.112553493203808 25.6564873335230 Trimmed Mean ( 4 / 24 ) 2.8921875 0.110044739447461 26.2819241930309 Trimmed Mean ( 5 / 24 ) 2.89516129032258 0.107713543252826 26.8783404843255 Trimmed Mean ( 6 / 24 ) 2.89816666666667 0.105327439851576 27.5157800355792 Trimmed Mean ( 7 / 24 ) 2.89913793103448 0.103073542391453 28.1268874996468 Trimmed Mean ( 8 / 24 ) 2.90214285714286 0.101115118362241 28.7013742766541 Trimmed Mean ( 9 / 24 ) 2.89629629629630 0.100770718399113 28.741447340141 Trimmed Mean ( 10 / 24 ) 2.88980769230769 0.100324695482850 28.8045498508558 Trimmed Mean ( 11 / 24 ) 2.8816 0.0999233828939933 28.8380949137504 Trimmed Mean ( 12 / 24 ) 2.87270833333333 0.099438021781547 28.8894356692284 Trimmed Mean ( 13 / 24 ) 2.86456521739130 0.099156201626227 28.8894206354272 Trimmed Mean ( 14 / 24 ) 2.85522727272727 0.0986716684997293 28.9366473288643 Trimmed Mean ( 15 / 24 ) 2.84595238095238 0.0982170080219625 28.9761665343745 Trimmed Mean ( 16 / 24 ) 2.83625 0.0977711138584818 29.0090793494008 Trimmed Mean ( 17 / 24 ) 2.82631578947368 0.0975346318861129 28.9775614550312 Trimmed Mean ( 18 / 24 ) 2.81583333333333 0.0972057015441914 28.9677795499805 Trimmed Mean ( 19 / 24 ) 2.80411764705882 0.096555764319701 29.0414318276664 Trimmed Mean ( 20 / 24 ) 2.790625 0.095510024701852 29.2181371401728 Trimmed Mean ( 21 / 24 ) 2.77766666666667 0.0944879525657987 29.3970457739824 Trimmed Mean ( 22 / 24 ) 2.76464285714286 0.0932305019444782 29.6538450344212 Trimmed Mean ( 23 / 24 ) 2.74961538461538 0.0915851529271333 30.0225014288399 Trimmed Mean ( 24 / 24 ) 2.7325 0.0889415416219382 30.7224267779726 Median 2.67 Midrange 2.625 Midmean - Weighted Average at Xnp 2.79864864864865 Midmean - Weighted Average at X(n+1)p 2.81583333333333 Midmean - Empirical Distribution Function 2.79864864864865 Midmean - Empirical Distribution Function - Averaging 2.81583333333333 Midmean - Empirical Distribution Function - Interpolation 2.81583333333333 Midmean - Closest Observation 2.79864864864865 Midmean - True Basic - Statistics Graphics Toolkit 2.81583333333333 Midmean - MS Excel (old versions) 2.82631578947368 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/27/t1256644198retfe9lfrjafdzb/14h991256644049.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256644198retfe9lfrjafdzb/14h991256644049.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256644198retfe9lfrjafdzb/20i4z1256644049.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256644198retfe9lfrjafdzb/20i4z1256644049.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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