*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 14 Apr 2010 10:52:35 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Apr/14/t1271242390gzfn5u0ttbxmfzf.htm/, Retrieved Wed, 14 Apr 2010 12:53:11 +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/2010/Apr/14/t1271242390gzfn5u0ttbxmfzf.htm/}, year = {2010}, } @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 = {2010}, 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 «

268 250 231 295 258 288 292 253 272 251 274 302 325 307 246 299 305 280 272 252 235 220 274 301 305 320 248 278 264 263 261 267 255 222 276 277 281 284 218 281 298 288 270 245 250 227 238 262 272 264 212 294 280 273 239 242 201 239 266 276 288 271 220 274 273 289 270 243 225 222 234 254

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 264.569444444444 3.18759002995928 82.9998343443884 Geometric Mean 263.177602060977 Harmonic Mean 261.756688076777 Quadratic Mean 265.929319139086 Winsorized Mean ( 1 / 24 ) 264.652777777778 3.13008020380414 84.5514365593994 Winsorized Mean ( 2 / 24 ) 264.458333333333 3.01112552979472 87.8270702156221 Winsorized Mean ( 3 / 24 ) 264.458333333333 2.97702059181136 88.8332227397945 Winsorized Mean ( 4 / 24 ) 264.458333333333 2.97702059181136 88.8332227397945 Winsorized Mean ( 5 / 24 ) 264.388888888889 2.90919939857535 90.8802913331968 Winsorized Mean ( 6 / 24 ) 264.305555555556 2.89417139217706 91.3233944160918 Winsorized Mean ( 7 / 24 ) 264.402777777778 2.8009513615593 94.3974898695076 Winsorized Mean ( 8 / 24 ) 264.513888888889 2.73825511987973 96.5994318675854 Winsorized Mean ( 9 / 24 ) 264.638888888889 2.58064797242332 102.547457738059 Winsorized Mean ( 10 / 24 ) 264.916666666667 2.48286380537804 106.698025921857 Winsorized Mean ( 11 / 24 ) 264.763888888889 2.40658761522365 110.016309904546 Winsorized Mean ( 12 / 24 ) 264.763888888889 2.24301149561615 118.039470331007 Winsorized Mean ( 13 / 24 ) 264.763888888889 2.18558847226374 121.140778444287 Winsorized Mean ( 14 / 24 ) 264.763888888889 2.18558847226374 121.140778444287 Winsorized Mean ( 15 / 24 ) 265.388888888889 2.08425383941562 127.330406628061 Winsorized Mean ( 16 / 24 ) 264.722222222222 1.91793917976302 138.024304949509 Winsorized Mean ( 17 / 24 ) 264.486111111111 1.74566230302297 151.510467203823 Winsorized Mean ( 18 / 24 ) 264.736111111111 1.70667852470246 155.117737335603 Winsorized Mean ( 19 / 24 ) 265 1.59088266953651 166.574194989003 Winsorized Mean ( 20 / 24 ) 265.555555555556 1.50869790277912 176.016388082985 Winsorized Mean ( 21 / 24 ) 264.972222222222 1.43194225298819 185.04393013704 Winsorized Mean ( 22 / 24 ) 264.972222222222 1.34835612866027 196.515013051856 Winsorized Mean ( 23 / 24 ) 264.972222222222 1.26218198898827 209.93186761809 Winsorized Mean ( 24 / 24 ) 265.305555555556 1.21426041699677 218.491479951011 Trimmed Mean ( 1 / 24 ) 264.614285714286 3.02674707738399 87.4253047740583 Trimmed Mean ( 2 / 24 ) 264.573529411765 2.90365609022239 91.117377950741 Trimmed Mean ( 3 / 24 ) 264.636363636364 2.83350223247877 93.3955020761913 Trimmed Mean ( 4 / 24 ) 264.703125 2.76481217317318 95.7400027272739 Trimmed Mean ( 5 / 24 ) 264.774193548387 2.68172609856218 98.732750406668 Trimmed Mean ( 6 / 24 ) 264.866666666667 2.60285226716201 101.760161346176 Trimmed Mean ( 7 / 24 ) 264.98275862069 2.51065381218042 105.543327931206 Trimmed Mean ( 8 / 24 ) 265.089285714286 2.42300618071076 109.405121548854 Trimmed Mean ( 9 / 24 ) 265.185185185185 2.3307973751412 113.774448183905 Trimmed Mean ( 10 / 24 ) 265.269230769231 2.25539664262122 117.615334596284 Trimmed Mean ( 11 / 24 ) 265.32 2.18406847466851 121.479707746008 Trimmed Mean ( 12 / 24 ) 265.395833333333 2.11121196062153 125.707810624189 Trimmed Mean ( 13 / 24 ) 265.478260869565 2.05568356237837 129.143544136926 Trimmed Mean ( 14 / 24 ) 265.568181818182 1.99613731835623 133.041038497728 Trimmed Mean ( 15 / 24 ) 265.666666666667 1.91717788465878 138.57173546207 Trimmed Mean ( 16 / 24 ) 265.7 1.83805917708368 144.554649443642 Trimmed Mean ( 17 / 24 ) 265.815789473684 1.77298169793722 149.925850776096 Trimmed Mean ( 18 / 24 ) 265.972222222222 1.72630723925475 154.070038156732 Trimmed Mean ( 19 / 24 ) 266.117647058824 1.67010236212292 159.342117641552 Trimmed Mean ( 20 / 24 ) 266.25 1.62142907894996 164.206997059917 Trimmed Mean ( 21 / 24 ) 266.333333333333 1.57373071155469 169.23691669601 Trimmed Mean ( 22 / 24 ) 266.5 1.5218861869856 175.111649135772 Trimmed Mean ( 23 / 24 ) 266.692307692308 1.46735683958421 181.750137729196 Trimmed Mean ( 24 / 24 ) 266.916666666667 1.40897314169208 189.440564030992 Median 269 Midrange 263 Midmean - Weighted Average at Xnp 265.815789473684 Midmean - Weighted Average at X(n+1)p 266.378378378378 Midmean - Empirical Distribution Function 265.815789473684 Midmean - Empirical Distribution Function - Averaging 266.378378378378 Midmean - Empirical Distribution Function - Interpolation 266.378378378378 Midmean - Closest Observation 265.815789473684 Midmean - True Basic - Statistics Graphics Toolkit 266.378378378378 Midmean - MS Excel (old versions) 265.815789473684 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Apr/14/t1271242390gzfn5u0ttbxmfzf/1a7wd1271242351.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/14/t1271242390gzfn5u0ttbxmfzf/1a7wd1271242351.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/14/t1271242390gzfn5u0ttbxmfzf/2a7wd1271242351.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/14/t1271242390gzfn5u0ttbxmfzf/2a7wd1271242351.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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