central tendency

*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: Fri, 11 Dec 2009 07:25:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t12605415663cq77u72ijtnprf.htm/, Retrieved Fri, 11 Dec 2009 15:26:08 +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/Dec/11/t12605415663cq77u72ijtnprf.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:

sdws paper

Dataseries X:

» Textbox « » Textfile « » CSV «

-1683.85608706230 -6999.35087749223 3931.32652673605 1822.75271017275 1412.85831010682 341.612129794388 -9381.55507514847 649.055948328826 1377.63729026095 -7846.62135114955 5098.26277502930 4768.34811151406 10740.5901250635 -3118.87364267085 -6653.8909673415 -12172.3430680778 1308.85607902947 3886.70335197895 -296.995134388884 1185.3316058715 -3756.67652699999 -2029.93703138424 -6049.80708904876 -155.869195324281 -8288.29444857815 579.977007038197 1553.52404432216 -785.985112768088 -1164.46843095385 -3530.73252748869 3994.02389637401 5628.36174903917 -2536.24819950515 -8281.44574137424 -4045.3675548633 -3055.43106194414 -15078.6790675691 -4042.4923457908 -5639.19325606102 8410.26835938425 -5007.38028583601 -6462.30324482812 1106.39886423720 -6829.95884874971 -11713.0921878395 7497.4340368301 5293.56561524665 -16151.1360566203 6574.13330938066 4743.47649440836 9426.5615899051 -2156.25032128639 -3480.8931163 etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -644.621081677988 735.526516714735 -0.8764076712791 Geometric Mean NaN Harmonic Mean 7599.28208526315 Quadratic Mean 6274.35118780105 Winsorized Mean ( 1 / 24 ) -639.893853964372 728.865640716097 -0.877931155234163 Winsorized Mean ( 2 / 24 ) -599.150103774865 699.601495583506 -0.856416270630098 Winsorized Mean ( 3 / 24 ) -583.766803517299 694.547898123264 -0.840498985159546 Winsorized Mean ( 4 / 24 ) -462.747133344728 666.89100604799 -0.693887200679129 Winsorized Mean ( 5 / 24 ) -478.294030529282 639.202395033444 -0.748266956202905 Winsorized Mean ( 6 / 24 ) -544.230282655472 618.746079602584 -0.879569666130291 Winsorized Mean ( 7 / 24 ) -631.105615634262 601.612876101695 -1.04902278641985 Winsorized Mean ( 8 / 24 ) -684.637269028755 574.900462626852 -1.19087966271672 Winsorized Mean ( 9 / 24 ) -651.843298614642 545.043392685035 -1.19594752888111 Winsorized Mean ( 10 / 24 ) -647.487314309434 538.137820385611 -1.20319979340137 Winsorized Mean ( 11 / 24 ) -655.147443041119 528.234686296263 -1.24025827920296 Winsorized Mean ( 12 / 24 ) -678.688551744539 514.305462734254 -1.31962151079702 Winsorized Mean ( 13 / 24 ) -652.574301431073 499.330860326713 -1.30689759692420 Winsorized Mean ( 14 / 24 ) -702.315132988344 487.275865758379 -1.44130908657930 Winsorized Mean ( 15 / 24 ) -623.0530338345 473.839621885444 -1.31490277523717 Winsorized Mean ( 16 / 24 ) -499.320292529275 451.715226708457 -1.10538733920418 Winsorized Mean ( 17 / 24 ) -642.521274023028 424.83162323674 -1.51241395150328 Winsorized Mean ( 18 / 24 ) -437.354077659765 392.840214357747 -1.11331289841289 Winsorized Mean ( 19 / 24 ) -448.219986536579 390.953457642973 -1.1464791467477 Winsorized Mean ( 20 / 24 ) -465.128365227096 385.197188903017 -1.20750716419222 Winsorized Mean ( 21 / 24 ) -572.114934264435 349.455021635758 -1.63716329382371 Winsorized Mean ( 22 / 24 ) -951.256358754229 288.664130029712 -3.29537431150977 Winsorized Mean ( 23 / 24 ) -1030.48555990765 276.765964998629 -3.72331027015102 Winsorized Mean ( 24 / 24 ) -1036.71147971749 265.56095035708 -3.90385513503964 Trimmed Mean ( 1 / 24 ) -616.807767809406 697.779803590037 -0.883957610461016 Trimmed Mean ( 2 / 24 ) -592.38335781937 660.583119760035 -0.896758242981687 Trimmed Mean ( 3 / 24 ) -588.69699621675 635.330170064725 -0.926600095438212 Trimmed Mean ( 4 / 24 ) -590.542658099108 607.39187733567 -0.972259722486789 Trimmed Mean ( 5 / 24 ) -627.56279027002 584.321510762718 -1.07400254604842 Trimmed Mean ( 6 / 24 ) -663.289411453869 565.505764992475 -1.17291361558922 Trimmed Mean ( 7 / 24 ) -687.841152703256 548.615616552147 -1.25377610835450 Trimmed Mean ( 8 / 24 ) -698.221338683298 532.550361180099 -1.31108978526666 Trimmed Mean ( 9 / 24 ) -700.475059330529 519.419423271085 -1.34857309516697 Trimmed Mean ( 10 / 24 ) -707.917655834218 509.993109778284 -1.38809258843120 Trimmed Mean ( 11 / 24 ) -716.567489032864 499.512570158136 -1.43453344688806 Trimmed Mean ( 12 / 24 ) -724.885973925994 488.274211656296 -1.48458787423378 Trimmed Mean ( 13 / 24 ) -730.865427506218 476.847366798973 -1.53270307942024 Trimmed Mean ( 14 / 24 ) -740.635089392518 465.24310202316 -1.59193137130199 Trimmed Mean ( 15 / 24 ) -745.281861514619 452.65069771103 -1.64648340383296 Trimmed Mean ( 16 / 24 ) -759.790323987218 438.922368011908 -1.73103578072058 Trimmed Mean ( 17 / 24 ) -790.26197830842 425.504785507363 -1.8572340552319 Trimmed Mean ( 18 / 24 ) -807.408355753307 413.910538926211 -1.95068325113907 Trimmed Mean ( 19 / 24 ) -850.287660992717 405.006977966332 -2.09943953376379 Trimmed Mean ( 20 / 24 ) -897.099367907068 392.272549697821 -2.28692874022954 Trimmed Mean ( 21 / 24 ) -947.960469835516 375.119954526258 -2.52708622507887 Trimmed Mean ( 22 / 24 ) -993.012561948306 361.275268788475 -2.74863143906402 Trimmed Mean ( 23 / 24 ) -998.144216549598 359.814355506321 -2.77405334521753 Trimmed Mean ( 24 / 24 ) -994.038272088489 358.999910860283 -2.76890952342145 Median -785.985112768088 Midrange -1631.99372401265 Midmean - Weighted Average at Xnp -939.0398802669 Midmean - Weighted Average at X(n+1)p -807.408355753306 Midmean - Empirical Distribution Function -807.408355753306 Midmean - Empirical Distribution Function - Averaging -807.408355753306 Midmean - Empirical Distribution Function - Interpolation -807.408355753306 Midmean - Closest Observation -916.164238168484 Midmean - True Basic - Statistics Graphics Toolkit -807.408355753306 Midmean - MS Excel (old versions) -807.408355753306 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605415663cq77u72ijtnprf/1ptub1260541504.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605415663cq77u72ijtnprf/1ptub1260541504.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605415663cq77u72ijtnprf/2fftx1260541504.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605415663cq77u72ijtnprf/2fftx1260541504.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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