*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 02 Dec 2009 10:55:45 -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/02/t12597766477k1hooir071t5qo.htm/, Retrieved Wed, 02 Dec 2009 18:57:29 +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/Dec/02/t12597766477k1hooir071t5qo.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 «

104.0 99.0 105.4 107.1 110.7 117.1 118.7 126.5 127.5 134.6 131.8 135.9 142.7 141.7 153.4 145.0 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179.0 190.6 190.0 181.6 174.8 180.5 196.8 193.8 197.0 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244.0 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191.0 159.7 163.4 157.6 166.2 176.7 198.3 226.2 216.2 235.9

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 203.719178082192 8.42199380615913 24.1889489319274 Geometric Mean 192.501099940956 Harmonic Mean 182.364264969619 Quadratic Mean 215.889930415465 Winsorized Mean ( 1 / 24 ) 203.698630136986 8.3800011745073 24.3077090199767 Winsorized Mean ( 2 / 24 ) 203.082191780822 8.16280622168205 24.87896763265 Winsorized Mean ( 3 / 24 ) 202.309589041096 7.90316275927765 25.5985603742757 Winsorized Mean ( 4 / 24 ) 201.684931506849 7.64539601196232 26.3799195216682 Winsorized Mean ( 5 / 24 ) 201.171232876712 7.32815027489829 27.4518432797156 Winsorized Mean ( 6 / 24 ) 200.324657534247 7.06724247590057 28.3455192343205 Winsorized Mean ( 7 / 24 ) 200.152054794521 6.7338428052173 29.7233037040076 Winsorized Mean ( 8 / 24 ) 198.409589041096 6.30435909096893 31.4718096127043 Winsorized Mean ( 9 / 24 ) 197.978082191781 6.02022758769706 32.8854813722274 Winsorized Mean ( 10 / 24 ) 197.772602739726 5.84133021988352 33.8574597386261 Winsorized Mean ( 11 / 24 ) 195.316438356164 5.29573146426661 36.8818622458631 Winsorized Mean ( 12 / 24 ) 193.064383561644 4.80212502502252 40.2039477430595 Winsorized Mean ( 13 / 24 ) 192.672602739726 4.51055428134271 42.7159481345098 Winsorized Mean ( 14 / 24 ) 191.982191780822 4.343750362161 44.1973354300479 Winsorized Mean ( 15 / 24 ) 191.735616438356 4.16210726334928 46.0669570260102 Winsorized Mean ( 16 / 24 ) 192.195890410959 4.01199278948851 47.9053429294578 Winsorized Mean ( 17 / 24 ) 192.289041095890 3.75699832096428 51.1815616267129 Winsorized Mean ( 18 / 24 ) 192.215068493151 3.66037269648076 52.512430954901 Winsorized Mean ( 19 / 24 ) 192.709589041096 3.41699695718578 56.3973545940205 Winsorized Mean ( 20 / 24 ) 192.956164383562 3.28928023793093 58.6621237553592 Winsorized Mean ( 21 / 24 ) 192.668493150685 3.13679183261951 61.4221483067905 Winsorized Mean ( 22 / 24 ) 193.271232876712 3.02835375772601 63.8205600596146 Winsorized Mean ( 23 / 24 ) 193.491780821918 2.81713996822140 68.6837654516964 Winsorized Mean ( 24 / 24 ) 193.130136986301 2.55469744083307 75.5980469152241 Trimmed Mean ( 1 / 24 ) 202.238028169014 7.99441640312462 25.2974098384429 Trimmed Mean ( 2 / 24 ) 200.692753623188 7.52733362966 26.6618650769507 Trimmed Mean ( 3 / 24 ) 199.391044776119 7.10694162904155 28.0558157339206 Trimmed Mean ( 4 / 24 ) 198.298461538462 6.72402534126254 29.4910342353391 Trimmed Mean ( 5 / 24 ) 197.317460317460 6.36066402179597 31.0215190806048 Trimmed Mean ( 6 / 24 ) 196.395081967213 6.02623836047085 32.5899956522576 Trimmed Mean ( 7 / 24 ) 195.584745762712 5.69762519538547 34.3274152046921 Trimmed Mean ( 8 / 24 ) 194.749122807018 5.3876425734073 36.1473724645866 Trimmed Mean ( 9 / 24 ) 194.141818181818 5.12404623031756 37.8883814578282 Trimmed Mean ( 10 / 24 ) 193.554716981132 4.86913918926084 39.751321426183 Trimmed Mean ( 11 / 24 ) 192.950980392157 4.5929275319898 42.0104560867226 Trimmed Mean ( 12 / 24 ) 192.630612244898 4.38573484181784 43.9220835715309 Trimmed Mean ( 13 / 24 ) 192.574468085106 4.2422149060173 45.3947931331702 Trimmed Mean ( 14 / 24 ) 192.562222222222 4.12404784099764 46.6925287112189 Trimmed Mean ( 15 / 24 ) 192.632558139535 4.00685697010149 48.0757260807979 Trimmed Mean ( 16 / 24 ) 192.739024390244 3.89290768193995 49.5102992769139 Trimmed Mean ( 17 / 24 ) 192.802564102564 3.77487697591047 51.075191412314 Trimmed Mean ( 18 / 24 ) 192.862162162162 3.67556118440308 52.4714873420026 Trimmed Mean ( 19 / 24 ) 192.937142857143 3.55987226122041 54.1977713523349 Trimmed Mean ( 20 / 24 ) 192.963636363636 3.46028281539738 55.7652789260453 Trimmed Mean ( 21 / 24 ) 192.964516129032 3.349362155252 57.6123175651377 Trimmed Mean ( 22 / 24 ) 193 3.22908960922943 59.7691682040549 Trimmed Mean ( 23 / 24 ) 192.966666666667 3.08019590896534 62.647530342148 Trimmed Mean ( 24 / 24 ) 192.9 2.92554268469971 65.9364845397222 Median 193.8 Midrange 256.3 Midmean - Weighted Average at Xnp 191.838888888889 Midmean - Weighted Average at X(n+1)p 192.862162162162 Midmean - Empirical Distribution Function 192.862162162162 Midmean - Empirical Distribution Function - Averaging 192.862162162162 Midmean - Empirical Distribution Function - Interpolation 192.862162162162 Midmean - Closest Observation 191.792105263158 Midmean - True Basic - Statistics Graphics Toolkit 192.862162162162 Midmean - MS Excel (old versions) 192.862162162162 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t12597766477k1hooir071t5qo/1kiif1259776544.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t12597766477k1hooir071t5qo/1kiif1259776544.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t12597766477k1hooir071t5qo/2yulc1259776544.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t12597766477k1hooir071t5qo/2yulc1259776544.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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