*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: Sat, 24 Oct 2009 04:10:39 -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/24/t1256379343q863c2jegk1u7l4.htm/, Retrieved Sat, 24 Oct 2009 12:15:44 +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/24/t1256379343q863c2jegk1u7l4.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:

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69,78206203 64,19822724 59,43536404 53,80982368 64,13934426 64,37601297 67,2 58,96084337 60,57206538 61,12573099 59,2679558 58,69734284 66,94053208 62,82089552 59,70385675 60,11963406 62,46715328 56,2804878 61,62393162 59,53793103 64,12837345 63,24287653 60,98208361 60,10222489 58,62831858 58,16274309 57,57653061 50,66896849 47,48563218 51,86721992 55,22606383 56,1206517 48,70980392 51,86528497 49,68446602 46,84115523 49,17371253 48,61561119 46,91392582 49,36257968 50,08178439 49,2609017 52,50601443 52,1339076 55,53719008 53,90199637 55,03133705 56,58369408 56,71466845 53,21407795 49,0327381 53,03166069 51,26201923 52,68386714 53,38838269 51,87606595 60,54860088 71,66123779 72,58706468 78,50655903

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 57.266019821 0.888553852666524 64.4485639774633 Geometric Mean 56.8748292416914 Harmonic Mean 56.4982428704264 Quadratic Mean 57.671302873573 Winsorized Mean ( 1 / 20 ) 57.168574425 0.853113467262717 67.011689088006 Winsorized Mean ( 2 / 20 ) 57.1567704073333 0.840068400139178 68.038234026972 Winsorized Mean ( 3 / 20 ) 57.1193105698333 0.803147641320004 71.1193155917828 Winsorized Mean ( 4 / 20 ) 56.9534526165 0.759225831734463 75.0151670766905 Winsorized Mean ( 5 / 20 ) 56.9587414715 0.749423278538687 76.003432376113 Winsorized Mean ( 6 / 20 ) 56.7163870035 0.693727782993331 81.7559688308536 Winsorized Mean ( 7 / 20 ) 56.7058174048333 0.688002545562004 82.4209412750245 Winsorized Mean ( 8 / 20 ) 56.7115234048333 0.684078022041203 82.9021275023765 Winsorized Mean ( 9 / 20 ) 56.7581607343333 0.675090479396018 84.0748943535881 Winsorized Mean ( 10 / 20 ) 56.6767976426667 0.636824575045648 88.9990742562095 Winsorized Mean ( 11 / 20 ) 56.7070848758333 0.604871025493053 93.7507046723047 Winsorized Mean ( 12 / 20 ) 56.7549465758333 0.573155069890900 99.0219742566991 Winsorized Mean ( 13 / 20 ) 56.7029561265 0.522201149860153 108.584510282456 Winsorized Mean ( 14 / 20 ) 56.5871608011667 0.503967163635833 112.283428136315 Winsorized Mean ( 15 / 20 ) 56.5534604636667 0.498169198751915 113.522595546558 Winsorized Mean ( 16 / 20 ) 56.5128800423333 0.471050812362615 119.971940519295 Winsorized Mean ( 17 / 20 ) 56.6116620358333 0.453680747146026 124.783038275177 Winsorized Mean ( 18 / 20 ) 56.5363278028333 0.426879790464006 132.440862898147 Winsorized Mean ( 19 / 20 ) 56.6409495231667 0.409437851443429 138.338332236468 Winsorized Mean ( 20 / 20 ) 56.5689658965 0.381596980126827 148.242698036286 Trimmed Mean ( 1 / 20 ) 57.0795426724138 0.821864286987391 69.4512994130009 Trimmed Mean ( 2 / 20 ) 56.9841515089286 0.783088536531933 72.7684659531533 Trimmed Mean ( 3 / 20 ) 56.8882521209259 0.74362086270482 76.5016891995238 Trimmed Mean ( 4 / 20 ) 56.7993834867308 0.712818484603166 79.6828150694655 Trimmed Mean ( 5 / 20 ) 56.7531627478 0.69216822595547 81.9933083022668 Trimmed Mean ( 6 / 20 ) 56.701768066875 0.669190607293942 84.7318648062984 Trimmed Mean ( 7 / 20 ) 56.6985900371739 0.65743864423162 86.2416448054104 Trimmed Mean ( 8 / 20 ) 56.6971821084091 0.643368792436127 88.125477603171 Trimmed Mean ( 9 / 20 ) 56.694621162619 0.625605691597586 90.6235699643973 Trimmed Mean ( 10 / 20 ) 56.684031234 0.604233567742497 93.8114567943977 Trimmed Mean ( 11 / 20 ) 56.68517338 0.586079042937744 96.719331740414 Trimmed Mean ( 12 / 20 ) 56.6818534563889 0.569811184280114 99.4747997584488 Trimmed Mean ( 13 / 20 ) 56.6711044682353 0.555522111967437 102.014129136154 Trimmed Mean ( 14 / 20 ) 56.6665104790625 0.548667310755242 103.280274527493 Trimmed Mean ( 15 / 20 ) 56.6778461473333 0.542139057310512 104.544849486598 Trimmed Mean ( 16 / 20 ) 56.6956155307143 0.53218309093984 106.534041565637 Trimmed Mean ( 17 / 20 ) 56.7219716107692 0.523684199273076 108.313314951081 Trimmed Mean ( 18 / 20 ) 56.7381936070833 0.513999025790018 110.385799895003 Trimmed Mean ( 19 / 20 ) 56.768779335 0.505260971170145 112.355362029107 Trimmed Mean ( 20 / 20 ) 56.7889629895 0.49432913923084 114.880872848932 Median 56.649181265 Midrange 62.67385713 Midmean - Weighted Average at Xnp 56.522664656129 Midmean - Weighted Average at X(n+1)p 56.6778461473333 Midmean - Empirical Distribution Function 56.522664656129 Midmean - Empirical Distribution Function - Averaging 56.6778461473333 Midmean - Empirical Distribution Function - Interpolation 56.6778461473333 Midmean - Closest Observation 56.522664656129 Midmean - True Basic - Statistics Graphics Toolkit 56.6778461473333 Midmean - MS Excel (old versions) 56.6665104790625 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/24/t1256379343q863c2jegk1u7l4/1vrhp1256379034.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256379343q863c2jegk1u7l4/1vrhp1256379034.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256379343q863c2jegk1u7l4/2ygqx1256379034.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256379343q863c2jegk1u7l4/2ygqx1256379034.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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