central tendency mannen

*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: Tue, 22 Dec 2009 08:51:24 -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/22/t1261497153gja4db6l5ms4bn0.htm/, Retrieved Tue, 22 Dec 2009 16:52:35 +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/22/t1261497153gja4db6l5ms4bn0.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 «

244.576 241.572 240.541 236.089 236.997 264.579 270.349 269.645 267.037 258.113 262.813 267.413 267.366 264.777 258.863 254.844 254.868 277.267 285.351 286.602 283.042 276.687 277.915 277.128 277.103 275.037 270.150 267.140 264.993 287.259 291.186 292.300 288.186 281.477 282.656 280.190 280.408 276.836 275.216 274.352 271.311 289.802 290.726 292.300 278.506 269.826 265.861 269.034 264.176 255.198 253.353 246.057 235.372 258.556 260.993 254.663 250.643 243.422 247.105 248.541 245.039 237.080 237.085 225.554 226.839 247.934 248.333 246.969 245.098 246.263 255.765 264.319 268.347 273.046 273.963 267.430 271.993 292.710 295.881

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 264.607797468354 1.94358006192638 136.144531759648 Geometric Mean 264.043440600968 Harmonic Mean 263.471742023818 Quadratic Mean 265.163971441651 Winsorized Mean ( 1 / 26 ) 264.583924050633 1.93155919924945 136.979453776743 Winsorized Mean ( 2 / 26 ) 264.789569620253 1.88082613305244 140.783650847365 Winsorized Mean ( 3 / 26 ) 264.816797468354 1.87542257909303 141.203801436806 Winsorized Mean ( 4 / 26 ) 264.806367088608 1.85605369003289 142.671717154860 Winsorized Mean ( 5 / 26 ) 264.782506329114 1.84977479184619 143.143104499140 Winsorized Mean ( 6 / 26 ) 264.712708860760 1.83724870490755 144.081042568529 Winsorized Mean ( 7 / 26 ) 264.875746835443 1.75574143544627 150.862616492341 Winsorized Mean ( 8 / 26 ) 264.886278481013 1.72158903418932 153.861504238579 Winsorized Mean ( 9 / 26 ) 265.022189873418 1.67341908730728 158.371678609133 Winsorized Mean ( 10 / 26 ) 265.009911392405 1.62373154109783 163.210422834570 Winsorized Mean ( 11 / 26 ) 264.752873417722 1.56335930574095 169.348704706269 Winsorized Mean ( 12 / 26 ) 264.703202531646 1.55316819632722 170.427905462904 Winsorized Mean ( 13 / 26 ) 264.667 1.49951566582931 176.501657189174 Winsorized Mean ( 14 / 26 ) 264.514063291139 1.46692373418509 180.318892609698 Winsorized Mean ( 15 / 26 ) 264.606721518987 1.43995929834657 183.759861700828 Winsorized Mean ( 16 / 26 ) 264.293202531646 1.38956760177026 190.198161064596 Winsorized Mean ( 17 / 26 ) 264.344417721519 1.34489968081147 196.553260806800 Winsorized Mean ( 18 / 26 ) 264.287683544304 1.31178372625996 201.471994394851 Winsorized Mean ( 19 / 26 ) 264.304278481013 1.29975966231885 203.348577543542 Winsorized Mean ( 20 / 26 ) 264.830101265823 1.21778631238300 217.468449573552 Winsorized Mean ( 21 / 26 ) 265.479506329114 1.10384755182971 240.503777798902 Winsorized Mean ( 22 / 26 ) 265.80282278481 1.04777392252169 253.683372979067 Winsorized Mean ( 23 / 26 ) 265.427253164557 0.984706936711054 269.549490583554 Winsorized Mean ( 24 / 26 ) 265.380164556962 0.976790066971192 271.685977909099 Winsorized Mean ( 25 / 26 ) 265.26782278481 0.935135769164223 283.667710649004 Winsorized Mean ( 26 / 26 ) 265.326405063291 0.893547460831191 296.935995785250 Trimmed Mean ( 1 / 26 ) 264.708844155844 1.88407080458058 140.498352563120 Trimmed Mean ( 2 / 26 ) 264.840426666667 1.82837935594659 144.849823317740 Trimmed Mean ( 3 / 26 ) 264.867945205479 1.79479088421769 147.575936302423 Trimmed Mean ( 4 / 26 ) 264.886915492958 1.75743588069297 150.723516233498 Trimmed Mean ( 5 / 26 ) 264.909971014493 1.71999431477815 154.017934093382 Trimmed Mean ( 6 / 26 ) 264.940029850746 1.67724048782195 157.961861625935 Trimmed Mean ( 7 / 26 ) 264.986076923077 1.62947075768420 162.620946508837 Trimmed Mean ( 8 / 26 ) 265.005841269841 1.59281098765659 166.376201145956 Trimmed Mean ( 9 / 26 ) 265.025196721311 1.55634907336138 170.286474453263 Trimmed Mean ( 10 / 26 ) 265.025644067797 1.52258254832367 174.063235099853 Trimmed Mean ( 11 / 26 ) 265.027824561404 1.49159815473699 177.680445446874 Trimmed Mean ( 12 / 26 ) 265.063727272727 1.46538451038253 180.883396401900 Trimmed Mean ( 13 / 26 ) 265.108509433962 1.43426476960646 184.839309346421 Trimmed Mean ( 14 / 26 ) 265.161117647059 1.40564429150229 188.640269270162 Trimmed Mean ( 15 / 26 ) 265.235632653061 1.37527102081447 192.860627933527 Trimmed Mean ( 16 / 26 ) 265.306106382979 1.34153162230658 197.763587508151 Trimmed Mean ( 17 / 26 ) 265.417244444444 1.30749460595506 202.996817910825 Trimmed Mean ( 18 / 26 ) 265.533186046512 1.27208239791409 208.738983010789 Trimmed Mean ( 19 / 26 ) 265.666512195122 1.23174476941369 215.683085320978 Trimmed Mean ( 20 / 26 ) 265.811743589744 1.17976890662268 225.308314278838 Trimmed Mean ( 21 / 26 ) 265.811743589744 1.1312975300483 234.961834998787 Trimmed Mean ( 22 / 26 ) 265.963514285714 1.09528579162250 242.825677389395 Trimmed Mean ( 23 / 26 ) 265.981 1.05926637616882 251.099256980107 Trimmed Mean ( 24 / 26 ) 266.042354838710 1.02414144431007 259.771105169885 Trimmed Mean ( 25 / 26 ) 266.117517241379 0.973485573404821 273.365650721066 Trimmed Mean ( 26 / 26 ) 266.216962962963 0.910685100239975 292.326033326791 Median 267.14 Midrange 260.7175 Midmean - Weighted Average at Xnp 265.379975 Midmean - Weighted Average at X(n+1)p 265.666512195122 Midmean - Empirical Distribution Function 265.666512195122 Midmean - Empirical Distribution Function - Averaging 265.666512195122 Midmean - Empirical Distribution Function - Interpolation 265.811743589744 Midmean - Closest Observation 265.379975 Midmean - True Basic - Statistics Graphics Toolkit 265.666512195122 Midmean - MS Excel (old versions) 265.666512195122 Number of observations 79

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/22/t1261497153gja4db6l5ms4bn0/1pr6p1261497081.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/22/t1261497153gja4db6l5ms4bn0/1pr6p1261497081.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/22/t1261497153gja4db6l5ms4bn0/2kx4o1261497081.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/22/t1261497153gja4db6l5ms4bn0/2kx4o1261497081.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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