ws3 central tendency Yt/Xt

*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, 27 Oct 2009 15:40:21 -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/27/t1256679770rz15gnx6n41x7el.htm/, Retrieved Tue, 27 Oct 2009 22:42:50 +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/Oct/27/t1256679770rz15gnx6n41x7el.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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1.207317073 1.225 1.24 1.220588235 1.230769231 1.287878788 1.368421053 1.3875 1.345679012 1.298701299 1.226666667 1.210526316 1.217948718 1.230769231 1.217948718 1.213333333 1.186666667 1.267605634 1.346666667 1.373333333 1.342105263 1.246753247 1.194805195 1.17721519 1.160493827 1.146341463 1.12195122 1.097560976 1.139240506 1.232876712 1.420289855 1.515151515 1.462686567 1.347826087 1.285714286 1.267605634 1.263888889 1.281690141 1.31884058 1.314285714 1.294117647 1.296875 1.253731343 1.227272727 1.203125 1.253968254 1.274193548 1.230769231 1.161764706 1.117647059 1.109375 1.114754098 1.120689655 1.131147541 1.138888889 1.191780822 1.202898551 1.295081967 1.293103448 1.258064516 1.169014085

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.24555583490164 0.0112994007843796 110.232025456032 Geometric Mean 1.24255134641633 Harmonic Mean 1.23961270453399 Quadratic Mean 1.24862721632306 Winsorized Mean ( 1 / 20 ) 1.24488942631148 0.0109441629537734 113.749167622021 Winsorized Mean ( 2 / 20 ) 1.24367573404918 0.0104814052859236 118.655437903867 Winsorized Mean ( 3 / 20 ) 1.242205395 0.010030297428542 123.845320026623 Winsorized Mean ( 4 / 20 ) 1.24147594772131 0.00977240893007823 127.038886379407 Winsorized Mean ( 5 / 20 ) 1.24117670878689 0.00966165396286755 128.464206393344 Winsorized Mean ( 6 / 20 ) 1.24005553059016 0.00905392744832124 136.963272311188 Winsorized Mean ( 7 / 20 ) 1.24081083380328 0.00885315617826452 140.154630599380 Winsorized Mean ( 8 / 20 ) 1.24072741898361 0.00881855708914338 140.695060024171 Winsorized Mean ( 9 / 20 ) 1.24124782672131 0.00851639729240068 145.747994616092 Winsorized Mean ( 10 / 20 ) 1.23975400393443 0.00737267397333536 168.155272892607 Winsorized Mean ( 11 / 20 ) 1.23916180955738 0.00718657732980586 172.427256076134 Winsorized Mean ( 12 / 20 ) 1.23752213034426 0.00641984045672519 192.765246844706 Winsorized Mean ( 13 / 20 ) 1.23888069555738 0.00605387363801774 204.642641989969 Winsorized Mean ( 14 / 20 ) 1.24063837122951 0.00563005912705481 220.359741031443 Winsorized Mean ( 15 / 20 ) 1.24165882245902 0.0053942951120561 230.179995099627 Winsorized Mean ( 16 / 20 ) 1.24218608121311 0.00523012390054549 237.506052406055 Winsorized Mean ( 17 / 20 ) 1.24298555386885 0.00466272527460546 266.5791957846 Winsorized Mean ( 18 / 20 ) 1.24241366937705 0.0045512389482143 272.983616881842 Winsorized Mean ( 19 / 20 ) 1.24246597481967 0.00416771913358887 298.116532087365 Winsorized Mean ( 20 / 20 ) 1.24106028629508 0.00364058938298693 340.895430859289 Trimmed Mean ( 1 / 20 ) 1.24349480403390 0.0104327870837774 119.191045887199 Trimmed Mean ( 2 / 20 ) 1.24200231352632 0.0097958609853531 126.788478867082 Trimmed Mean ( 3 / 20 ) 1.24107432578182 0.00932530074643569 133.086788247144 Trimmed Mean ( 4 / 20 ) 1.24064039356604 0.00896676084635504 138.359928944726 Trimmed Mean ( 5 / 20 ) 1.24039054649020 0.00862261817180998 143.853122308653 Trimmed Mean ( 6 / 20 ) 1.24019480812245 0.00822643448221207 150.757270455883 Trimmed Mean ( 7 / 20 ) 1.24022493553191 0.00792231985019555 156.548202923327 Trimmed Mean ( 8 / 20 ) 1.24011147586667 0.00759101403896342 163.365720245198 Trimmed Mean ( 9 / 20 ) 1.24000225339535 0.00716729947162459 173.008293891518 Trimmed Mean ( 10 / 20 ) 1.23979634560976 0.00669799030800876 185.099752104349 Trimmed Mean ( 11 / 20 ) 1.23980296828205 0.00641767966873598 193.185548715030 Trimmed Mean ( 12 / 20 ) 1.23989906332432 0.0060899518492336 203.597515057588 Trimmed Mean ( 13 / 20 ) 1.24024428454286 0.00586357605379449 211.516704680629 Trimmed Mean ( 14 / 20 ) 1.24043817481818 0.00565191946221771 219.472018861970 Trimmed Mean ( 15 / 20 ) 1.24041003661290 0.00547287787987295 226.646759500086 Trimmed Mean ( 16 / 20 ) 1.24023491951724 0.00527629791500504 235.057788528239 Trimmed Mean ( 17 / 20 ) 1.23995940825926 0.00502763544285669 246.628742746454 Trimmed Mean ( 18 / 20 ) 1.23952506736 0.00484252801450045 255.966524849907 Trimmed Mean ( 19 / 20 ) 1.23909945208696 0.00457857860385982 270.629721425416 Trimmed Mean ( 20 / 20 ) 1.23858477066667 0.00430332708197831 287.820271866778 Median 1.230769231 Midrange 1.3063562455 Midmean - Weighted Average at Xnp 1.23861978293333 Midmean - Weighted Average at X(n+1)p 1.24041003661290 Midmean - Empirical Distribution Function 1.24041003661290 Midmean - Empirical Distribution Function - Averaging 1.24041003661290 Midmean - Empirical Distribution Function - Interpolation 1.24041003661290 Midmean - Closest Observation 1.2387305563125 Midmean - True Basic - Statistics Graphics Toolkit 1.24041003661290 Midmean - MS Excel (old versions) 1.24041003661290 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/27/t1256679770rz15gnx6n41x7el/13t1l1256679617.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256679770rz15gnx6n41x7el/13t1l1256679617.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256679770rz15gnx6n41x7el/2ycpq1256679617.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/27/t1256679770rz15gnx6n41x7el/2ycpq1256679617.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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