*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 22 Oct 2009 14:37:51 -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/22/t125624524194fq2t9l1shg35d.htm/, Retrieved Thu, 22 Oct 2009 23:00:42 +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/22/t125624524194fq2t9l1shg35d.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0,64 0,69 0,73 0,68 0,67 0,60 0,61 0,64 0,59 0,58 0,54 0,55 0,57 0,59 0,57 0,53 0,54 0,53 0,48 0,47 0,48 0,46 0,46 0,51 0,53 0,53 0,51 0,55 0,52 0,50 0,48 0,47 0,46 0,44 0,45 0,43 0,40 0,38 0,38 0,37 0,35 0,33 0,32 0,29 0,28 0,27 0,31 0,35 0,47 0,58 0,70 0,68 0,71 0,67 0,63 0,56 0,49 0,51 0,47 0,49

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.5095 0.0149167652996771 34.1561987310366 Geometric Mean 0.495535763267674 Harmonic Mean 0.480402813428653 Quadratic Mean 0.522224408978873 Winsorized Mean ( 1 / 20 ) 0.509333333333333 0.0147920933733312 34.4328095069773 Winsorized Mean ( 2 / 20 ) 0.509333333333333 0.0146307984626091 34.8124085390829 Winsorized Mean ( 3 / 20 ) 0.509833333333333 0.014276312146778 35.7118370690989 Winsorized Mean ( 4 / 20 ) 0.509833333333333 0.0139803972258065 36.4677287131892 Winsorized Mean ( 5 / 20 ) 0.510666666666667 0.0137919706983404 37.0263741009917 Winsorized Mean ( 6 / 20 ) 0.511666666666667 0.0131552371188620 38.8945225421318 Winsorized Mean ( 7 / 20 ) 0.511666666666667 0.0131552371188620 38.8945225421318 Winsorized Mean ( 8 / 20 ) 0.510333333333333 0.0118273041057777 43.1487453750371 Winsorized Mean ( 9 / 20 ) 0.511833333333333 0.0115310724082855 44.3873141378909 Winsorized Mean ( 10 / 20 ) 0.510166666666667 0.0112231894382839 45.4564782562088 Winsorized Mean ( 11 / 20 ) 0.510166666666667 0.00986774597089626 51.7004256262111 Winsorized Mean ( 12 / 20 ) 0.514166666666667 0.00844487497663512 60.8850537265783 Winsorized Mean ( 13 / 20 ) 0.514166666666667 0.00771780415284163 66.6208492058398 Winsorized Mean ( 14 / 20 ) 0.5165 0.00734856533136765 70.2858281459782 Winsorized Mean ( 15 / 20 ) 0.5165 0.00655625375323714 78.7797451776449 Winsorized Mean ( 16 / 20 ) 0.5165 0.00655625375323714 78.7797451776449 Winsorized Mean ( 17 / 20 ) 0.513666666666667 0.0061016190620939 84.1853058080605 Winsorized Mean ( 18 / 20 ) 0.516666666666667 0.00566816198283478 91.1524173499837 Winsorized Mean ( 19 / 20 ) 0.5135 0.00517395148907481 99.2471616875987 Winsorized Mean ( 20 / 20 ) 0.510166666666667 0.00467890847927578 109.035401937512 Trimmed Mean ( 1 / 20 ) 0.509827586206896 0.0143596770655584 35.5041122359023 Trimmed Mean ( 2 / 20 ) 0.510357142857143 0.0138262978435794 36.9120605263208 Trimmed Mean ( 3 / 20 ) 0.510925925925926 0.0132736307967939 38.491798796252 Trimmed Mean ( 4 / 20 ) 0.511346153846154 0.0127601993811577 40.0735238197949 Trimmed Mean ( 5 / 20 ) 0.5118 0.0122347447701959 41.8316858760106 Trimmed Mean ( 6 / 20 ) 0.512083333333333 0.0116348032459558 44.0130634363181 Trimmed Mean ( 7 / 20 ) 0.512173913043478 0.0110812242451295 46.2199754931042 Trimmed Mean ( 8 / 20 ) 0.512272727272727 0.0103575795512784 49.458729690326 Trimmed Mean ( 9 / 20 ) 0.512619047619048 0.00983050033291954 52.1457738933625 Trimmed Mean ( 10 / 20 ) 0.51275 0.00921945754564212 55.6160704099525 Trimmed Mean ( 11 / 20 ) 0.513157894736842 0.0084848225568051 60.4795081218608 Trimmed Mean ( 12 / 20 ) 0.513611111111111 0.00791976408356523 64.8518195355006 Trimmed Mean ( 13 / 20 ) 0.513529411764706 0.00758648710672671 67.6900131167922 Trimmed Mean ( 14 / 20 ) 0.5134375 0.00733156805335446 70.0310624225991 Trimmed Mean ( 15 / 20 ) 0.513 0.00706537615629098 72.6075991783151 Trimmed Mean ( 16 / 20 ) 0.5125 0.00691262551671878 74.1397026007665 Trimmed Mean ( 17 / 20 ) 0.511923076923077 0.00665684681117537 76.9017361288338 Trimmed Mean ( 18 / 20 ) 0.511666666666667 0.00641744301721699 79.7306131575996 Trimmed Mean ( 19 / 20 ) 0.510909090909091 0.00616894508894584 82.8195231992891 Trimmed Mean ( 20 / 20 ) 0.5105 0.00595929172760798 85.6645425890085 Median 0.51 Midrange 0.5 Midmean - Weighted Average at Xnp 0.510967741935484 Midmean - Weighted Average at X(n+1)p 0.513 Midmean - Empirical Distribution Function 0.510967741935484 Midmean - Empirical Distribution Function - Averaging 0.513 Midmean - Empirical Distribution Function - Interpolation 0.513 Midmean - Closest Observation 0.510967741935484 Midmean - True Basic - Statistics Graphics Toolkit 0.513 Midmean - MS Excel (old versions) 0.515757575757576 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/22/t125624524194fq2t9l1shg35d/1xb501256243866.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t125624524194fq2t9l1shg35d/1xb501256243866.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t125624524194fq2t9l1shg35d/2feps1256243866.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t125624524194fq2t9l1shg35d/2feps1256243866.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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