central tendency - Part 2 y/x

*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: Tue, 20 Oct 2009 12:32:47 -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/20/t1256063694oo6t97mr5xxsg9h.htm/, Retrieved Tue, 20 Oct 2009 20:34:57 +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/20/t1256063694oo6t97mr5xxsg9h.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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1,140392008 1,137504274 1,159834936 1,147433743 1,142575967 1,132101412 1,126931141 1,124906831 1,121414029 1,124189564 1,147332194 1,16088965 1,159732954 1,149271297 1,124034478 1,11528473 1,112606844 1,117877155 1,104333685 1,094377176 1,086379426 1,087737651 1,144925934 1,137897599 1,152573213 1,120821074 1,109918637 1,096691942 1,096110373 1,083662288 1,077607353 1,083374478 1,075834902 1,076909009 1,118612239 1,147937004 1,163241926 1,126956016 1,102871415 1,094494335 1,081131503 1,079825864 1,071347826 1,077872448 1,067794251 1,080907455 1,105369888 1,131127639 1,148687448 1,097206532 1,06519025 1,037926932 1,018028268 0,998426144 0,984885242 0,964218483 0,958421393 0,957884306 0,971425735 1,003928803 1,01633089 0,979287348

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 1.09233557306452 0.0070624827169323 154.667362292532 Geometric Mean 1.09088985294940 Harmonic Mean 1.08938954441804 Quadratic Mean 1.09372738951346 Winsorized Mean ( 1 / 20 ) 1.09230629582258 0.00705363717971765 154.857170562082 Winsorized Mean ( 2 / 20 ) 1.09245927569355 0.00699102192539391 156.266034830379 Winsorized Mean ( 3 / 20 ) 1.09280307908065 0.0068874125689993 158.66670801738 Winsorized Mean ( 4 / 20 ) 1.09284836114516 0.00667262383280951 163.780903663652 Winsorized Mean ( 5 / 20 ) 1.09303352066129 0.00650975355911414 167.907050664147 Winsorized Mean ( 6 / 20 ) 1.09428742901613 0.00615563586391051 177.770006739963 Winsorized Mean ( 7 / 20 ) 1.09482396941935 0.00598669003317289 182.876341242459 Winsorized Mean ( 8 / 20 ) 1.09635930180645 0.00558977190286894 196.136679788982 Winsorized Mean ( 9 / 20 ) 1.09659095440323 0.00552995101753663 198.300301562474 Winsorized Mean ( 10 / 20 ) 1.09941230988710 0.00475388674209176 231.265987082255 Winsorized Mean ( 11 / 20 ) 1.10383242054839 0.00375284698865212 294.132008015825 Winsorized Mean ( 12 / 20 ) 1.103913719 0.00359790287405468 306.821433941583 Winsorized Mean ( 13 / 20 ) 1.10413580219355 0.00339130738206937 325.578214476037 Winsorized Mean ( 14 / 20 ) 1.10506019758065 0.00322095165717495 343.084999465617 Winsorized Mean ( 15 / 20 ) 1.10401291814516 0.00297278240861026 371.373604387437 Winsorized Mean ( 16 / 20 ) 1.10394183969355 0.00290720635625428 379.725999607367 Winsorized Mean ( 17 / 20 ) 1.10287069491935 0.00272567026772589 404.62366559089 Winsorized Mean ( 18 / 20 ) 1.10343059391935 0.00264041281752111 417.900786800181 Winsorized Mean ( 19 / 20 ) 1.10314169616129 0.00250247187946950 440.820816094504 Winsorized Mean ( 20 / 20 ) 1.10298259325806 0.00245909272659849 448.532331183684 Trimmed Mean ( 1 / 20 ) 1.09339465496667 0.00683685895256228 159.926460755328 Trimmed Mean ( 2 / 20 ) 1.09455807336207 0.00656801829690993 166.649668725349 Trimmed Mean ( 3 / 20 ) 1.09571990778571 0.00627539039526305 174.605855376394 Trimmed Mean ( 4 / 20 ) 1.09683622494444 0.00596044530829588 184.019174442863 Trimmed Mean ( 5 / 20 ) 1.09802491511538 0.00565072460231236 194.315772293354 Trimmed Mean ( 6 / 20 ) 1.09926278094 0.00531370170008254 206.873257661966 Trimmed Mean ( 7 / 20 ) 1.10033386364583 0.00500491343557592 219.85072825125 Trimmed Mean ( 8 / 20 ) 1.10139477495652 0.00465729557918777 236.488055402445 Trimmed Mean ( 9 / 20 ) 1.10228170488636 0.00433220576836776 254.438907988821 Trimmed Mean ( 10 / 20 ) 1.10321510840476 0.00391134985480951 282.054827452527 Trimmed Mean ( 11 / 20 ) 1.103804542175 0.00360982032187034 305.778250370947 Trimmed Mean ( 12 / 20 ) 1.10380040710526 0.00351118561176385 314.366863263251 Trimmed Mean ( 13 / 20 ) 1.10378414475 0.00341546049005906 323.172862916331 Trimmed Mean ( 14 / 20 ) 1.10373481723529 0.00333544158668012 330.911151807602 Trimmed Mean ( 15 / 20 ) 1.1035513940625 0.00326309139035586 338.191997111718 Trimmed Mean ( 16 / 20 ) 1.1034878063 0.00322303879425794 342.374968699086 Trimmed Mean ( 17 / 20 ) 1.10342497132143 0.00317139851668202 347.930089995707 Trimmed Mean ( 18 / 20 ) 1.1035027205 0.00313709182940023 351.759776413996 Trimmed Mean ( 19 / 20 ) 1.103513072 0.00309493138472168 356.554939294474 Trimmed Mean ( 20 / 20 ) 1.10356815645455 0.00305739248669925 360.950764828350 Median 1.10360255 Midrange 1.060563116 Midmean - Weighted Average at Xnp 1.10263042574194 Midmean - Weighted Average at X(n+1)p 1.1035513940625 Midmean - Empirical Distribution Function 1.1035513940625 Midmean - Empirical Distribution Function - Averaging 1.1035513940625 Midmean - Empirical Distribution Function - Interpolation 1.1034878063 Midmean - Closest Observation 1.1035513940625 Midmean - True Basic - Statistics Graphics Toolkit 1.1035513940625 Midmean - MS Excel (old versions) 1.1035513940625 Number of observations 62

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256063694oo6t97mr5xxsg9h/1urvi1256063565.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256063694oo6t97mr5xxsg9h/1urvi1256063565.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256063694oo6t97mr5xxsg9h/26wxa1256063565.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256063694oo6t97mr5xxsg9h/26wxa1256063565.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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