workshop 3 deel 2.3 central tendency

*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, 21 Oct 2009 09:20:00 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138461ttg5wik9ao79jlk.htm/, Retrieved Wed, 21 Oct 2009 17:21:01 +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/2009/Oct/21/t1256138461ttg5wik9ao79jlk.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:

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User-defined keywords:

workshop 3 deel 2.3 central tendency

Dataseries X:

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0,399934319 0,402094483 0,413840465 0,41769597 0,421773812 0,421728159 0,420448844 0,418168871 0,41394247 0,419491756 0,418931641 0,431121329 0,437504246 0,436747812 0,434770429 0,430466243 0,429993174 0,434192053 0,437475305 0,449428904 0,456433147 0,464477714 0,460451751 0,470616958 0,455674518 0,452604032 0,454019481 0,450387747 0,450519858 0,444374599 0,451595471 0,442070639 0,430214821 0,428359923 0,427941082 0,436084416 0,437256451 0,435992141 0,435055566 0,441513836 0,448230261 0,459135121 0,452356157 0,451658155 0,444926134 0,446837485 0,441311793 0,442769291 0,434637126 0,441366029 0,441312468 0,437274135 0,43987734 0,439724254 0,438800956 0,442739125 0,438363286 0,439328277 0,441090932 0,439025957 0,440138453 0,438464971 0,42896355 0,426178903 0,423034344 0,423294812 0,421353873 0,410653049 0,412040464 0,421861821 0,414864122 0,412795347 0,408402345 0,407074304 0,413636086 0,418130501 0,416700587 0,430063694 0,434329797 0 etc...

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.4342414971125 0.00171257369710909 253.560765207081 Geometric Mean 0.433974075135941 Harmonic Mean 0.433706018674372 Quadratic Mean 0.434508201993104 Winsorized Mean ( 1 / 26 ) 0.4341917586125 0.00168684821316333 257.398238456953 Winsorized Mean ( 2 / 26 ) 0.4342338119875 0.00164083780314619 264.641521029615 Winsorized Mean ( 3 / 26 ) 0.4342563031375 0.00162497935896688 267.238042588792 Winsorized Mean ( 4 / 26 ) 0.4343030068375 0.00158981696826438 273.177991873890 Winsorized Mean ( 5 / 26 ) 0.4342208469 0.00154163839369143 281.661931018898 Winsorized Mean ( 6 / 26 ) 0.43422056595 0.00152116708633599 285.452249033273 Winsorized Mean ( 7 / 26 ) 0.434149314875 0.00148295131943596 292.760328127377 Winsorized Mean ( 8 / 26 ) 0.434028207875 0.00145592959739750 298.110711294579 Winsorized Mean ( 9 / 26 ) 0.4340117975 0.0014494312370041 299.435934882348 Winsorized Mean ( 10 / 26 ) 0.43403975375 0.00141559214111748 306.61356554817 Winsorized Mean ( 11 / 26 ) 0.4342836486375 0.00137207705406495 316.515495504338 Winsorized Mean ( 12 / 26 ) 0.4342716141375 0.00132268543558696 328.325694419387 Winsorized Mean ( 13 / 26 ) 0.4343207573875 0.00130821579672549 331.994735482189 Winsorized Mean ( 14 / 26 ) 0.4341596746125 0.00128145797764768 338.801335810846 Winsorized Mean ( 15 / 26 ) 0.434077948425 0.00122558721741507 354.179565727301 Winsorized Mean ( 16 / 26 ) 0.433911416225 0.00116818676895155 371.44010509076 Winsorized Mean ( 17 / 26 ) 0.4337086353375 0.00108132878886651 401.088586379108 Winsorized Mean ( 18 / 26 ) 0.4337881714875 0.00103382410992783 419.595719737839 Winsorized Mean ( 19 / 26 ) 0.4334958037625 0.000972478273477472 445.763998626281 Winsorized Mean ( 20 / 26 ) 0.4334996755125 0.000969820894353471 446.989416330828 Winsorized Mean ( 21 / 26 ) 0.4333473003 0.000945444436617137 458.353006815023 Winsorized Mean ( 22 / 26 ) 0.4335166233 0.000878518003397652 493.463562070877 Winsorized Mean ( 23 / 26 ) 0.4335490133375 0.000862340476939262 502.758510045025 Winsorized Mean ( 24 / 26 ) 0.4343981723375 0.00073369533282854 592.068877776296 Winsorized Mean ( 25 / 26 ) 0.4349486423375 0.00065736790962544 661.651772118491 Winsorized Mean ( 26 / 26 ) 0.4350129858375 0.00063030958556506 690.157655539253 Trimmed Mean ( 1 / 26 ) 0.434214980666667 0.00163400079365841 265.737313195847 Trimmed Mean ( 2 / 26 ) 0.434239424934211 0.00157213490463801 276.210027303093 Trimmed Mean ( 3 / 26 ) 0.434242458959459 0.00152872204861987 284.055861790896 Trimmed Mean ( 4 / 26 ) 0.434237331486111 0.00148478100750899 292.458840253236 Trimmed Mean ( 5 / 26 ) 0.4342185671 0.00144560751203036 300.370995229638 Trimmed Mean ( 6 / 26 ) 0.434218030676471 0.00141392538032191 307.101093678374 Trimmed Mean ( 7 / 26 ) 0.4342175185 0.00138161205567140 314.28324377858 Trimmed Mean ( 8 / 26 ) 0.43422969771875 0.00135228825365427 321.10735011218 Trimmed Mean ( 9 / 26 ) 0.434262196080645 0.00132301051506870 328.237902219617 Trimmed Mean ( 10 / 26 ) 0.434299292166667 0.00128874794136950 336.993199543082 Trimmed Mean ( 11 / 26 ) 0.434335090568966 0.00125419489228769 346.305899696916 Trimmed Mean ( 12 / 26 ) 0.434341771339286 0.00122095542382522 355.739253754657 Trimmed Mean ( 13 / 26 ) 0.434350432722222 0.00118996470233130 365.011190559913 Trimmed Mean ( 14 / 26 ) 0.434353944596154 0.00115410531836189 376.355552379452 Trimmed Mean ( 15 / 26 ) 0.43437614688 0.00111449079437323 389.753014626099 Trimmed Mean ( 16 / 26 ) 0.434409280041667 0.00107613495787255 403.675465482940 Trimmed Mean ( 17 / 26 ) 0.434463395673913 0.00103920035975939 418.074716385303 Trimmed Mean ( 18 / 26 ) 0.434544118704545 0.00100981104912847 430.322206396517 Trimmed Mean ( 19 / 26 ) 0.434624113119048 0.000981364524597304 442.877342950004 Trimmed Mean ( 20 / 26 ) 0.434742882525 0.000955820106409247 454.837557412565 Trimmed Mean ( 21 / 26 ) 0.434873746421053 0.000920918657635995 472.217326487202 Trimmed Mean ( 22 / 26 ) 0.435035275111111 0.00087757396017406 495.72491306012 Trimmed Mean ( 23 / 26 ) 0.435197697764706 0.000835636944336822 520.797579276593 Trimmed Mean ( 24 / 26 ) 0.43537690259375 0.000779478290200602 558.549106584744 Trimmed Mean ( 25 / 26 ) 0.4354856504 0.000744741564274495 584.747342286766 Trimmed Mean ( 26 / 26 ) 0.43554702275 0.000719684384921262 605.191708859504 Median 0.436416114 Midrange 0.4352756385 Midmean - Weighted Average at Xnp 0.434425450243902 Midmean - Weighted Average at X(n+1)p 0.434742882525 Midmean - Empirical Distribution Function 0.434425450243902 Midmean - Empirical Distribution Function - Averaging 0.434742882525 Midmean - Empirical Distribution Function - Interpolation 0.434742882525 Midmean - Closest Observation 0.434425450243902 Midmean - True Basic - Statistics Graphics Toolkit 0.434742882525 Midmean - MS Excel (old versions) 0.434624113119048 Number of observations 80

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138461ttg5wik9ao79jlk/1ej541256138395.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138461ttg5wik9ao79jlk/1ej541256138395.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138461ttg5wik9ao79jlk/201p81256138395.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256138461ttg5wik9ao79jlk/201p81256138395.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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