*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 11:00:53 -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/t1256662889x1bm80pz4hce1eg.htm/, Retrieved Tue, 27 Oct 2009 18:01:29 +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/t1256662889x1bm80pz4hce1eg.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 «

104,28 104,33 104,46 104,46 104,5 104,61 104,66 104,66 105,03 105,32 105,52 105,67 105,71 105,81 106 106,02 106,19 106,22 106,34 106,42 106,84 107,23 107,42 107,63 107,69 107,81 107,92 108,06 108,21 108,44 108,55 108,66 109,23 109,7 109,94 110,13 110,39 110,46 110,67 110,89 110,98 111,12 111,33 111,43 111,87 112,22 112,47 112,64 112,84 113,03 113,09 113,27 113,44 113,51 113,66 113,62 114,01 114,55 114,77 114,87 115,11 115,09 115,24 115,27 115,41 115,59 115,6 115,68 116,2 116,55 116,73 117,04 117,12 117,28 117,48 117,66 117,92 118,12 118,17 118,39

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 110.905625 0.492962140808571 224.977976641552 Geometric Mean 110.819114607763 Harmonic Mean 110.732700002519 Quadratic Mean 110.992141968475 Winsorized Mean ( 1 / 26 ) 110.9035 0.492335017023309 225.260231682341 Winsorized Mean ( 2 / 26 ) 110.9055 0.491557776327823 225.620477064809 Winsorized Mean ( 3 / 26 ) 110.898 0.490181069618828 226.238846975947 Winsorized Mean ( 4 / 26 ) 110.887 0.487527162501963 227.447839892518 Winsorized Mean ( 5 / 26 ) 110.882625 0.484434739884826 228.890737741811 Winsorized Mean ( 6 / 26 ) 110.871375 0.481263886656462 230.375430349177 Winsorized Mean ( 7 / 26 ) 110.857375 0.478925245341066 231.471145191048 Winsorized Mean ( 8 / 26 ) 110.886375 0.47166367428249 235.096279501880 Winsorized Mean ( 9 / 26 ) 110.884125 0.46092623774055 240.568047381185 Winsorized Mean ( 10 / 26 ) 110.886625 0.453559199649864 244.481040370478 Winsorized Mean ( 11 / 26 ) 110.859125 0.443008528997175 250.241513974795 Winsorized Mean ( 12 / 26 ) 110.787125 0.430549222172806 257.315817320265 Winsorized Mean ( 13 / 26 ) 110.790375 0.426271309417599 259.905774919192 Winsorized Mean ( 14 / 26 ) 110.821875 0.421152506043261 263.139535939545 Winsorized Mean ( 15 / 26 ) 110.791875 0.41581737006197 266.443595137665 Winsorized Mean ( 16 / 26 ) 110.797875 0.406995540584144 272.233633913965 Winsorized Mean ( 17 / 26 ) 110.797875 0.405197197410788 273.441859193496 Winsorized Mean ( 18 / 26 ) 110.795625 0.397310015252493 278.86441505782 Winsorized Mean ( 19 / 26 ) 110.809875 0.393968389054715 281.265903759123 Winsorized Mean ( 20 / 26 ) 110.859875 0.37183582763581 298.141993752631 Winsorized Mean ( 21 / 26 ) 110.936 0.354462402712486 312.969723025839 Winsorized Mean ( 22 / 26 ) 110.92775 0.339355726834605 326.877495289962 Winsorized Mean ( 23 / 26 ) 110.832875 0.310920753556415 356.466635733565 Winsorized Mean ( 24 / 26 ) 110.745875 0.295211289584964 375.141056277681 Winsorized Mean ( 25 / 26 ) 110.770875 0.288758976722211 383.610152167019 Winsorized Mean ( 26 / 26 ) 110.770875 0.279683545955361 396.057889718259 Trimmed Mean ( 1 / 26 ) 110.894615384615 0.488957234564561 226.798189177776 Trimmed Mean ( 2 / 26 ) 110.885263157895 0.484836289016008 228.706608127333 Trimmed Mean ( 3 / 26 ) 110.874324324324 0.480312748333639 230.837771241724 Trimmed Mean ( 4 / 26 ) 110.865555555556 0.475423494965587 233.193261859262 Trimmed Mean ( 5 / 26 ) 110.859428571429 0.470400291444497 235.670407922162 Trimmed Mean ( 6 / 26 ) 110.853970588235 0.465178090440149 238.304367437739 Trimmed Mean ( 7 / 26 ) 110.850454545455 0.459607587350881 241.184996932671 Trimmed Mean ( 8 / 26 ) 110.84921875 0.453324049312295 244.52534322448 Trimmed Mean ( 9 / 26 ) 110.843225806452 0.447212281420447 247.853716034784 Trimmed Mean ( 10 / 26 ) 110.837166666667 0.441886434503388 250.827266945252 Trimmed Mean ( 11 / 26 ) 110.830344827586 0.436646252150496 253.82181635991 Trimmed Mean ( 12 / 26 ) 110.826607142857 0.432021319578677 256.530412089245 Trimmed Mean ( 13 / 26 ) 110.831481481481 0.428346683214407 258.742476187228 Trimmed Mean ( 14 / 26 ) 110.836346153846 0.42417829613439 261.296599010173 Trimmed Mean ( 15 / 26 ) 110.838 0.419513518061975 264.206027286172 Trimmed Mean ( 16 / 26 ) 110.843125 0.414210044132758 267.601248617897 Trimmed Mean ( 17 / 26 ) 110.848043478261 0.408728394463957 271.202209045537 Trimmed Mean ( 18 / 26 ) 110.853409090909 0.401571035209751 276.049314744544 Trimmed Mean ( 19 / 26 ) 110.859523809524 0.393480250576324 281.741011517477 Trimmed Mean ( 20 / 26 ) 110.86475 0.383141700288549 289.35704444728 Trimmed Mean ( 21 / 26 ) 110.865263157895 0.374093068657212 296.357437350657 Trimmed Mean ( 22 / 26 ) 110.857777777778 0.365473624243442 303.326342652665 Trimmed Mean ( 23 / 26 ) 110.850294117647 0.356811360181742 310.669184022575 Trimmed Mean ( 24 / 26 ) 110.8521875 0.351397766064270 315.460706371495 Trimmed Mean ( 25 / 26 ) 110.864 0.346750299372535 319.722867436928 Trimmed Mean ( 26 / 26 ) 110.874642857143 0.340555678089594 325.569796630946 Median 110.935 Midrange 111.335 Midmean - Weighted Average at Xnp 110.756341463415 Midmean - Weighted Average at X(n+1)p 110.86475 Midmean - Empirical Distribution Function 110.756341463415 Midmean - Empirical Distribution Function - Averaging 110.86475 Midmean - Empirical Distribution Function - Interpolation 110.86475 Midmean - Closest Observation 110.756341463415 Midmean - True Basic - Statistics Graphics Toolkit 110.86475 Midmean - MS Excel (old versions) 110.859523809524 Number of observations 80

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/27/t1256662889x1bm80pz4hce1eg/14v7c1256662847.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256662889x1bm80pz4hce1eg/14v7c1256662847.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256662889x1bm80pz4hce1eg/2po631256662847.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256662889x1bm80pz4hce1eg/2po631256662847.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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