Centrall tendency Werklozen

*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: Wed, 23 Dec 2009 14:14:22 -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/23/t1261602896tc9nu206ac9kn85.htm/, Retrieved Wed, 23 Dec 2009 22:14:58 +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/23/t1261602896tc9nu206ac9kn85.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:

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517.009 509.933 509.127 500.857 506.971 569.323 579.714 577.992 565.464 547.344 554.788 562.325 560.854 555.332 543.599 536.662 542.722 593.530 610.763 612.613 611.324 594.167 595.454 590.865 589.379 584.428 573.100 567.456 569.028 620.735 628.884 628.232 612.117 595.404 597.141 593.408 590.072 579.799 574.205 572.775 572.942 619.567 625.809 619.916 587.625 565.742 557.274 560.576 548.854 531.673 525.919 511.038 498.662 555.362 564.591 541.657 527.070 509.846 514.258 516.922 507.561 492.622 490.243 469.357 477.580 528.379 533.590 517.945 506.174 501.866 516.141 528.222 532.638 536.322 536.535 523.597 536.214 586.570 596.594

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 555.67529113924 4.47955058425736 124.047107112055 Geometric Mean 554.260489901923 Harmonic Mean 552.840632854515 Quadratic Mean 557.081866794064 Winsorized Mean ( 1 / 26 ) 555.771126582279 4.45324908298657 124.801266721319 Winsorized Mean ( 2 / 26 ) 556.030367088608 4.37353515385716 127.135223001060 Winsorized Mean ( 3 / 26 ) 555.928025316456 4.31808095159219 128.74423419771 Winsorized Mean ( 4 / 26 ) 556.192379746835 4.25484599134099 130.719744234865 Winsorized Mean ( 5 / 26 ) 556.309215189873 4.22688113457503 131.612221275724 Winsorized Mean ( 6 / 26 ) 555.857696202532 4.11659670182821 135.028455897968 Winsorized Mean ( 7 / 26 ) 556.19546835443 4.04646188735959 137.452293840178 Winsorized Mean ( 8 / 26 ) 556.195873417721 4.01955608662417 138.372462389210 Winsorized Mean ( 9 / 26 ) 556.19917721519 3.99782694124105 139.125376208138 Winsorized Mean ( 10 / 26 ) 554.673101265823 3.68757836409815 150.416627526091 Winsorized Mean ( 11 / 26 ) 554.697050632911 3.660577651711 151.532655064328 Winsorized Mean ( 12 / 26 ) 554.537101265823 3.63329343411484 152.626566315562 Winsorized Mean ( 13 / 26 ) 554.71070886076 3.60366751004189 153.929491917614 Winsorized Mean ( 14 / 26 ) 555.062126582279 3.48484353921612 159.278923238871 Winsorized Mean ( 15 / 26 ) 555.29870886076 3.41433599745576 162.637393998291 Winsorized Mean ( 16 / 26 ) 555.43217721519 3.38763127814263 163.958864354246 Winsorized Mean ( 17 / 26 ) 554.903670886076 3.30741335029236 167.775724445517 Winsorized Mean ( 18 / 26 ) 554.936253164557 3.25108265903040 170.692754188557 Winsorized Mean ( 19 / 26 ) 556.128924050633 3.03509454707685 183.232817108202 Winsorized Mean ( 20 / 26 ) 556.272721518987 2.89310938938719 192.275039291485 Winsorized Mean ( 21 / 26 ) 556.298240506329 2.81332575580024 197.736874003804 Winsorized Mean ( 22 / 26 ) 556.022544303797 2.68914675042273 206.765415169846 Winsorized Mean ( 23 / 26 ) 554.720569620253 2.50513235137735 221.433637753814 Winsorized Mean ( 24 / 26 ) 555.695455696203 2.36923693392496 234.546172963637 Winsorized Mean ( 25 / 26 ) 555.455898734177 2.25934723302443 245.847955823340 Winsorized Mean ( 26 / 26 ) 554.522860759494 2.06259722292932 268.846895843268 Trimmed Mean ( 1 / 26 ) 555.845545454545 4.35200158059879 127.721816079411 Trimmed Mean ( 2 / 26 ) 555.923933333333 4.23351372519109 131.315018544847 Trimmed Mean ( 3 / 26 ) 555.866342465753 4.14428908263696 134.128274206215 Trimmed Mean ( 4 / 26 ) 555.843464788732 4.06349670143682 136.789446535589 Trimmed Mean ( 5 / 26 ) 555.743594202899 3.98978259077099 139.291698622482 Trimmed Mean ( 6 / 26 ) 555.610208955224 3.90993734951486 142.102074608475 Trimmed Mean ( 7 / 26 ) 555.560076923077 3.84382278600927 144.53321806229 Trimmed Mean ( 8 / 26 ) 555.446253968254 3.78050500497773 146.923824525270 Trimmed Mean ( 9 / 26 ) 555.324901639344 3.709106089243 149.719336216852 Trimmed Mean ( 10 / 26 ) 555.194830508475 3.62618253229770 153.107248618475 Trimmed Mean ( 11 / 26 ) 555.267140350877 3.58894053587884 154.716171750365 Trimmed Mean ( 12 / 26 ) 555.341581818182 3.54591068533093 156.614655895190 Trimmed Mean ( 13 / 26 ) 555.441509433962 3.49537163699557 158.907712002661 Trimmed Mean ( 14 / 26 ) 555.528588235294 3.4358382051405 161.686480872162 Trimmed Mean ( 15 / 26 ) 555.582306122449 3.38227547424466 164.262878749261 Trimmed Mean ( 16 / 26 ) 555.614085106383 3.32558608841809 167.072531076974 Trimmed Mean ( 17 / 26 ) 555.634044444444 3.25554794391153 170.672972420382 Trimmed Mean ( 18 / 26 ) 555.712976744186 3.17902793313536 174.805943336303 Trimmed Mean ( 19 / 26 ) 555.79612195122 3.08858883302816 179.951476871170 Trimmed Mean ( 20 / 26 ) 555.760641025641 3.01592070581462 184.275614393358 Trimmed Mean ( 21 / 26 ) 555.760641025641 2.9477393825943 188.537916312166 Trimmed Mean ( 22 / 26 ) 555.642314285714 2.8698991461129 193.610397437937 Trimmed Mean ( 23 / 26 ) 555.600939393939 2.79011314019924 199.132046435315 Trimmed Mean ( 24 / 26 ) 555.698483870968 2.72262547342445 204.103902389492 Trimmed Mean ( 25 / 26 ) 555.698827586207 2.65871378773571 209.010398242026 Trimmed Mean ( 26 / 26 ) 555.727259259259 2.59053261559424 214.522394319201 Median 557.274 Midrange 549.1205 Midmean - Weighted Average at Xnp 554.95655 Midmean - Weighted Average at X(n+1)p 555.79612195122 Midmean - Empirical Distribution Function 555.79612195122 Midmean - Empirical Distribution Function - Averaging 555.79612195122 Midmean - Empirical Distribution Function - Interpolation 555.760641025641 Midmean - Closest Observation 554.95655 Midmean - True Basic - Statistics Graphics Toolkit 555.79612195122 Midmean - MS Excel (old versions) 555.79612195122 Number of observations 79

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/23/t1261602896tc9nu206ac9kn85/13fqm1261602859.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/23/t1261602896tc9nu206ac9kn85/13fqm1261602859.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/23/t1261602896tc9nu206ac9kn85/233fm1261602859.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/23/t1261602896tc9nu206ac9kn85/233fm1261602859.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')

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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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