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WS2Q9BASISMETAAL

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

Title produced by software: Central Tendency

Date of computation: Sun, 21 Oct 2007 05:22:13 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Oct/21/oqbne80dfxjjfhi1192969314.htm/, Retrieved Sun, 21 Oct 2007 14:21:56 +0200

User-defined keywords:

WS2Q9BASISMETAAL

Dataseries X:

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2,354 2,318 2,25 2,219 2,206 2,146 2,212 2,243 2,275 2,291 2,141 2,134 2,18 2,183 2,169 2,132 2,092 2,069 2,099 2,073 2,051 2,082 2,059 2,101 2,158 2,153 2,145 2,149 2,135 2,097 2,143 2,13 2,132 2,142 2,094 2,147 2,203 2,244 2,26 2,254 2,231 2,211 2,209 2,191 2,21 2,257 2,252 2,266 2,264 2,265 2,255 2,28 2,288 2,284 2,282 2,271 2,296 2,303 2,316 2,325 2,415 2,402 2,425 2,4 2,424 2,393 2,419 2,415 2,425 2,421 2,378 2,364

Text written by user:

Output produced by software:

Summary of compuational 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 2.23336111111111 0.0125062473520562 178.579636899947 Geometric Mean 2.23089112209359 Harmonic Mean 2.22843836895438 Quadratic Mean 2.23584585659308 Winsorized Mean ( 1 / 24 ) 2.23347222222222 0.012483901561972 178.908189169461 Winsorized Mean ( 2 / 24 ) 2.23372222222222 0.0124246275677176 179.781825253742 Winsorized Mean ( 3 / 24 ) 2.23376388888889 0.012366999683195 180.622943811041 Winsorized Mean ( 4 / 24 ) 2.23415277777778 0.0122538464422392 182.322570166754 Winsorized Mean ( 5 / 24 ) 2.23456944444444 0.0120766304282099 185.032526889677 Winsorized Mean ( 6 / 24 ) 2.23473611111111 0.0120490649423172 185.469671033356 Winsorized Mean ( 7 / 24 ) 2.23376388888889 0.0117403690269393 190.263515888072 Winsorized Mean ( 8 / 24 ) 2.23376388888889 0.0116593117838786 191.586255715155 Winsorized Mean ( 9 / 24 ) 2.23313888888889 0.0114446908636886 195.124439400467 Winsorized Mean ( 10 / 24 ) 2.23508333333333 0.0104230121517783 214.437371921512 Winsorized Mean ( 11 / 24 ) 2.23325 0.00997531675910316 223.877602479340 Winsorized Mean ( 12 / 24 ) 2.23158333333333 0.00967285195509716 230.705829438172 Winsorized Mean ( 13 / 24 ) 2.22670833333333 0.00873551646144637 254.902883322442 Winsorized Mean ( 14 / 24 ) 2.22554166666667 0.0084941510185434 262.008723627369 Winsorized Mean ( 15 / 24 ) 2.226375 0.00824529641370895 270.017581939 Winsorized Mean ( 16 / 24 ) 2.22370833333333 0.00778389245862966 285.680762568605 Winsorized Mean ( 17 / 24 ) 2.22229166666667 0.00751611303822946 295.670335898802 Winsorized Mean ( 18 / 24 ) 2.22154166666667 0.00727145084951854 305.515599656946 Winsorized Mean ( 19 / 24 ) 2.22101388888889 0.0071266623697147 311.648535270488 Winsorized Mean ( 20 / 24 ) 2.22018055555556 0.00693992008329175 319.914426810298 Winsorized Mean ( 21 / 24 ) 2.22018055555556 0.00677821369560751 327.546556549892 Winsorized Mean ( 22 / 24 ) 2.22079166666667 0.00651998065117571 340.613229621503 Winsorized Mean ( 23 / 24 ) 2.22079166666667 0.00608449688210079 364.991832471758 Winsorized Mean ( 24 / 24 ) 2.223125 0.00539129803327251 412.354313614261 Trimmed Mean ( 1 / 24 ) 2.23322857142857 0.0122901965919411 181.708124416248 Trimmed Mean ( 2 / 24 ) 2.23297058823529 0.0120580788437913 185.184606699188 Trimmed Mean ( 3 / 24 ) 2.23256060606061 0.0118167856745112 188.931293801515 Trimmed Mean ( 4 / 24 ) 2.232109375 0.0115519254988896 193.224010595858 Trimmed Mean ( 5 / 24 ) 2.23151612903226 0.0112724948013177 197.961158409353 Trimmed Mean ( 6 / 24 ) 2.23078333333333 0.0109880801278668 203.018480696719 Trimmed Mean ( 7 / 24 ) 2.22996551724138 0.0106464938608390 209.455389388226 Trimmed Mean ( 8 / 24 ) 2.22926785714286 0.0103105195011718 216.212951916680 Trimmed Mean ( 9 / 24 ) 2.22851851851852 0.00991359388084564 224.794211393338 Trimmed Mean ( 10 / 24 ) 2.22780769230769 0.00947199724828121 235.199360167883 Trimmed Mean ( 11 / 24 ) 2.22676 0.00916415198655353 242.9859307514 Trimmed Mean ( 12 / 24 ) 2.225875 0.0088801927671397 250.65615785241 Trimmed Mean ( 13 / 24 ) 2.22513043478261 0.00858740841469785 259.115477840109 Trimmed Mean ( 14 / 24 ) 2.22493181818182 0.00842730371558214 264.014671035043 Trimmed Mean ( 15 / 24 ) 2.22485714285714 0.00826461127752588 269.202878168903 Trimmed Mean ( 16 / 24 ) 2.224675 0.00809711783955824 274.748996381331 Trimmed Mean ( 17 / 24 ) 2.22478947368421 0.00796990765412454 279.148714167704 Trimmed Mean ( 18 / 24 ) 2.22508333333333 0.00784496350411857 283.632082184343 Trimmed Mean ( 19 / 24 ) 2.2255 0.00771486631189022 288.469029796413 Trimmed Mean ( 20 / 24 ) 2.22603125 0.00754989910942523 294.842516136545 Trimmed Mean ( 21 / 24 ) 2.22673333333333 0.00734407781325899 303.201217355458 Trimmed Mean ( 22 / 24 ) 2.22753571428571 0.00707190621549707 314.983774728855 Trimmed Mean ( 23 / 24 ) 2.22838461538462 0.00673477243589667 330.877492386709 Trimmed Mean ( 24 / 24 ) 2.229375 0.0063604907351009 350.503615656102 Median 2.237 Midrange 2.238 Midmean - Weighted Average at Xnp 2.22286486486487 Midmean - Weighted Average at X(n+1)p 2.22508333333333 Midmean - Empirical Distribution Function 2.22286486486487 Midmean - Empirical Distribution Function - Averaging 2.22508333333333 Midmean - Empirical Distribution Function - Interpolation 2.22508333333333 Midmean - Closest Observation 2.22286486486487 Midmean - True Basic - Statistics Graphics Toolkit 2.22508333333333 Midmean - MS Excel (old versions) 2.22478947368421 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/oqbne80dfxjjfhi1192969314/1wm381192969331.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/oqbne80dfxjjfhi1192969314/1wm381192969331.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/oqbne80dfxjjfhi1192969314/2akav1192969331.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/oqbne80dfxjjfhi1192969314/2akav1192969331.ps (open in new window)

Parameters:

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')

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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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