central tendency biefstuk

*Unverified author*

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 07:03:23 -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/t1256389452wataavje8mcsdqn.htm/, Retrieved Sat, 24 Oct 2009 15:04:12 +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/t1256389452wataavje8mcsdqn.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 «

10,1200 10,1200 10,0500 10,1400 10,1700 10,2000 10,2000 10,3500 10,4300 10,5200 10,5700 10,5700 10,5700 10,6500 10,5700 10,6100 10,6300 10,7100 10,7200 10,7700 10,7900 10,8200 10,9000 10,8300 10,9200 10,9100 10,8800 10,8700 11,0000 10,9900 11,0300 11,0400 10,9900 10,9000 11,0000 10,9900 10,9200 10,9800 11,1500 11,1900 11,3300 11,3800 11,4000 11,4500 11,5600 11,6100 11,8200 11,7700 11,8500 11,8200 11,9200 11,8600 11,8700 11,9400 11,8600 11,9200 11,8300 11,9100 11,9300 11,9900 11,9600 12,1200 11,8500 12,0100 12,1000 12,2100 12,3100 12,3100 12,3900 12,3500 12,4100 12,5100

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 11.2405555555556 0.0812665990962663 138.317041448237 Geometric Mean 11.2197284505257 Harmonic Mean 11.1989575410599 Quadratic Mean 11.2613938598500 Winsorized Mean ( 1 / 24 ) 11.2401388888889 0.0807768650000199 139.150471968504 Winsorized Mean ( 2 / 24 ) 11.2395833333333 0.0806644059115553 139.337582745691 Winsorized Mean ( 3 / 24 ) 11.23875 0.0801724319079082 140.182226390608 Winsorized Mean ( 4 / 24 ) 11.2381944444444 0.0794255900205534 141.493370606832 Winsorized Mean ( 5 / 24 ) 11.2402777777778 0.0790351569476095 142.218706356574 Winsorized Mean ( 6 / 24 ) 11.2319444444444 0.0774997195433587 144.928839880001 Winsorized Mean ( 7 / 24 ) 11.2377777777778 0.0733664623797643 153.173226747776 Winsorized Mean ( 8 / 24 ) 11.2444444444444 0.0715201824522306 157.22057828858 Winsorized Mean ( 9 / 24 ) 11.2444444444444 0.0679296126343161 165.530819452429 Winsorized Mean ( 10 / 24 ) 11.2486111111111 0.0664698696127523 169.228722376688 Winsorized Mean ( 11 / 24 ) 11.2440277777778 0.0657583841867618 170.990025330357 Winsorized Mean ( 12 / 24 ) 11.2406944444444 0.0652512078413948 172.26799037601 Winsorized Mean ( 13 / 24 ) 11.2388888888889 0.0649796993565268 172.960001357101 Winsorized Mean ( 14 / 24 ) 11.2447222222222 0.0635777875005668 176.865579383711 Winsorized Mean ( 15 / 24 ) 11.2488888888889 0.062996558130499 178.563547322483 Winsorized Mean ( 16 / 24 ) 11.2511111111111 0.0620529569495265 181.314665153873 Winsorized Mean ( 17 / 24 ) 11.2558333333333 0.0587569294684752 191.566057572365 Winsorized Mean ( 18 / 24 ) 11.2558333333333 0.058063679224369 193.853257039374 Winsorized Mean ( 19 / 24 ) 11.2690277777778 0.0563832874751306 199.864681227541 Winsorized Mean ( 20 / 24 ) 11.2718055555556 0.0552863956093305 203.880275270708 Winsorized Mean ( 21 / 24 ) 11.2805555555556 0.054225911583354 208.028878190743 Winsorized Mean ( 22 / 24 ) 11.2775 0.0529603854372785 212.942181347151 Winsorized Mean ( 23 / 24 ) 11.2870833333333 0.0509938155982123 221.342200047667 Winsorized Mean ( 24 / 24 ) 11.2904166666667 0.050611455857407 223.080258716057 Trimmed Mean ( 1 / 24 ) 11.2394285714286 0.0797667110198668 140.903748289550 Trimmed Mean ( 2 / 24 ) 11.2386764705882 0.0785466382574865 143.082845044830 Trimmed Mean ( 3 / 24 ) 11.2381818181818 0.077145431966098 145.675272427284 Trimmed Mean ( 4 / 24 ) 11.23796875 0.0756739493583038 148.505117617029 Trimmed Mean ( 5 / 24 ) 11.2379032258065 0.0741595379937792 151.536855943589 Trimmed Mean ( 6 / 24 ) 11.2373333333333 0.0724334359017632 155.140139266261 Trimmed Mean ( 7 / 24 ) 11.2384482758621 0.0707550676357291 158.835948454200 Trimmed Mean ( 8 / 24 ) 11.2385714285714 0.0697497514641704 161.127046228180 Trimmed Mean ( 9 / 24 ) 11.2375925925926 0.0689047465273849 163.088802425627 Trimmed Mean ( 10 / 24 ) 11.2365384615385 0.0685905752617288 163.820443532685 Trimmed Mean ( 11 / 24 ) 11.2348 0.068406492113434 164.235873714589 Trimmed Mean ( 12 / 24 ) 11.2335416666667 0.0682113746359662 164.687220080498 Trimmed Mean ( 13 / 24 ) 11.2326086956522 0.0679488545812171 165.309757830078 Trimmed Mean ( 14 / 24 ) 11.2318181818182 0.0675447332215446 166.287105539053 Trimmed Mean ( 15 / 24 ) 11.2302380952381 0.0671793481616464 167.168012232211 Trimmed Mean ( 16 / 24 ) 11.228 0.0666758327032116 168.396847025192 Trimmed Mean ( 17 / 24 ) 11.2252631578947 0.0660603810634287 169.924287102078 Trimmed Mean ( 18 / 24 ) 11.2216666666667 0.0657924828050347 170.561532081412 Trimmed Mean ( 19 / 24 ) 11.2176470588235 0.0653689090045393 171.605236031162 Trimmed Mean ( 20 / 24 ) 11.2115625 0.0649148160417471 172.711919768667 Trimmed Mean ( 21 / 24 ) 11.2043333333333 0.064267192490814 174.339859873836 Trimmed Mean ( 22 / 24 ) 11.195 0.0632696003467884 176.941215665009 Trimmed Mean ( 23 / 24 ) 11.1846153846154 0.0618564859337403 180.815563894079 Trimmed Mean ( 24 / 24 ) 11.17125 0.0598921509580079 186.522771703966 Median 11.015 Midrange 11.28 Midmean - Weighted Average at Xnp 11.2078378378378 Midmean - Weighted Average at X(n+1)p 11.2216666666667 Midmean - Empirical Distribution Function 11.2078378378378 Midmean - Empirical Distribution Function - Averaging 11.2216666666667 Midmean - Empirical Distribution Function - Interpolation 11.2216666666667 Midmean - Closest Observation 11.2078378378378 Midmean - True Basic - Statistics Graphics Toolkit 11.2216666666667 Midmean - MS Excel (old versions) 11.2252631578947 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389452wataavje8mcsdqn/1ewin1256389398.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389452wataavje8mcsdqn/1ewin1256389398.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389452wataavje8mcsdqn/2d7sx1256389398.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389452wataavje8mcsdqn/2d7sx1256389398.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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