datareeks-diesel-seda hovhannesian

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 05 Aug 2009 15:26:17 -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/Aug/05/t12495076775km8f6b59rjqe4i.htm/, Retrieved Wed, 05 Aug 2009 23:28:00 +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/Aug/05/t12495076775km8f6b59rjqe4i.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:

» Textbox « » Textfile « » CSV «

0,9 0,92 0,92 0,95 1,06 1,17 1,23 1,26 1,37 1,37 1,31 1,21 1,2 1,11 1,11 1,11 1,17 1,08 1,05 1,03 1,04 1,02 1,01 1,01 0,98 0,96 0,94 0,99 0,99 0,98 1,02 1,06 1,06 1,06 1,06 1,06 1,04 1,02 1,01 1 1,04 1,09 1,08 1,06 1,06 1,03 0,97 0,98 0,93 0,88 0,86 0,9 0,91 0,93 0,89 0,88 0,83 0,81 0,83 0,8 0,76 0,73 0,74 0,74 0,75 0,74 0,74 0,73 0,71 0,71 0,7 0,75 0,81 0,78 0,75

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 0.969866666666667 0.0185991313691712 52.1458044150524 Geometric Mean 0.956636030074306 Harmonic Mean 0.94338655231831 Quadratic Mean 0.982975075981075 Winsorized Mean ( 1 / 25 ) 0.97 0.0185734480636465 52.2250901758283 Winsorized Mean ( 2 / 25 ) 0.9684 0.0181366584126839 53.3946208813608 Winsorized Mean ( 3 / 25 ) 0.9672 0.0175052733367575 55.2519221718792 Winsorized Mean ( 4 / 25 ) 0.9656 0.0171577104249672 56.2779051565587 Winsorized Mean ( 5 / 25 ) 0.964933333333333 0.0167647993873622 57.5571058763 Winsorized Mean ( 6 / 25 ) 0.964133333333333 0.0166090101818025 58.0488134319814 Winsorized Mean ( 7 / 25 ) 0.961333333333333 0.0160946897776577 59.729845471631 Winsorized Mean ( 8 / 25 ) 0.961333333333333 0.0160946897776577 59.729845471631 Winsorized Mean ( 9 / 25 ) 0.955333333333333 0.0147230692713431 64.8868327470812 Winsorized Mean ( 10 / 25 ) 0.955333333333333 0.0147230692713431 64.8868327470812 Winsorized Mean ( 11 / 25 ) 0.955333333333333 0.0147230692713431 64.8868327470812 Winsorized Mean ( 12 / 25 ) 0.953733333333333 0.0139842554109756 68.2005087367608 Winsorized Mean ( 13 / 25 ) 0.955466666666667 0.0131207741659825 72.8209063413232 Winsorized Mean ( 14 / 25 ) 0.9592 0.0124607636455649 76.9776257124825 Winsorized Mean ( 15 / 25 ) 0.9572 0.0116147777879331 82.4122525180348 Winsorized Mean ( 16 / 25 ) 0.9572 0.0116147777879331 82.4122525180347 Winsorized Mean ( 17 / 25 ) 0.961733333333333 0.0108542735940852 88.6041175392344 Winsorized Mean ( 18 / 25 ) 0.961733333333333 0.0108542735940852 88.6041175392344 Winsorized Mean ( 19 / 25 ) 0.969333333333333 0.00964660857799554 100.484364582226 Winsorized Mean ( 20 / 25 ) 0.974666666666667 0.0088517994980882 110.109437846754 Winsorized Mean ( 21 / 25 ) 0.974666666666667 0.0088517994980882 110.109437846754 Winsorized Mean ( 22 / 25 ) 0.9776 0.00843382293917589 115.914219097363 Winsorized Mean ( 23 / 25 ) 0.9776 0.00760710905062548 128.511369232918 Winsorized Mean ( 24 / 25 ) 0.9744 0.00720420297746673 135.254379012879 Winsorized Mean ( 25 / 25 ) 0.977733333333333 0.00674523076982086 144.951798789132 Trimmed Mean ( 1 / 25 ) 0.968082191780822 0.0179141126290956 54.040197905672 Trimmed Mean ( 2 / 25 ) 0.966056338028169 0.0171294971603775 56.397238575267 Trimmed Mean ( 3 / 25 ) 0.964782608695652 0.0164801266244289 58.5421842126825 Trimmed Mean ( 4 / 25 ) 0.963880597014925 0.0159997105693527 60.2436270854317 Trimmed Mean ( 5 / 25 ) 0.963384615384615 0.0155543045660211 61.936849140087 Trimmed Mean ( 6 / 25 ) 0.963015873015873 0.0151433412583457 63.5933547680664 Trimmed Mean ( 7 / 25 ) 0.962786885245902 0.0146901162779289 65.5397729351155 Trimmed Mean ( 8 / 25 ) 0.963050847457627 0.0142742902316803 67.4675119972157 Trimmed Mean ( 9 / 25 ) 0.963333333333333 0.0137634266487719 69.9922597705196 Trimmed Mean ( 10 / 25 ) 0.964545454545455 0.0134535444163051 71.6945233686127 Trimmed Mean ( 11 / 25 ) 0.965849056603774 0.0130629656388536 73.9379619686835 Trimmed Mean ( 12 / 25 ) 0.967254901960784 0.0125684897976617 76.9587211775228 Trimmed Mean ( 13 / 25 ) 0.968979591836735 0.0121051406476162 80.0469503035101 Trimmed Mean ( 14 / 25 ) 0.97063829787234 0.0117103662866673 82.8870996953742 Trimmed Mean ( 15 / 25 ) 0.972 0.0113555931130653 85.5965857812974 Trimmed Mean ( 16 / 25 ) 0.973720930232558 0.0110672126368710 87.98249045912 Trimmed Mean ( 17 / 25 ) 0.97560975609756 0.0106727872584610 91.4109625228534 Trimmed Mean ( 18 / 25 ) 0.977179487179487 0.0103380689898270 94.5224381981838 Trimmed Mean ( 19 / 25 ) 0.978918918918919 0.00986990286426962 99.1822242205379 Trimmed Mean ( 20 / 25 ) 0.98 0.00957061328523215 102.396781772823 Trimmed Mean ( 21 / 25 ) 0.98060606060606 0.00936364862213574 104.724781992342 Trimmed Mean ( 22 / 25 ) 0.981290322580645 0.0090487560540421 108.444775913956 Trimmed Mean ( 23 / 25 ) 0.981724137931035 0.00871085848502423 112.701192381764 Trimmed Mean ( 24 / 25 ) 0.982222222222222 0.00846197011762657 116.074886647995 Trimmed Mean ( 25 / 25 ) 0.9832 0.00817964954424495 120.200748782906 Median 0.99 Midrange 1.035 Midmean - Weighted Average at Xnp 0.97953488372093 Midmean - Weighted Average at X(n+1)p 0.97953488372093 Midmean - Empirical Distribution Function 0.97953488372093 Midmean - Empirical Distribution Function - Averaging 0.97953488372093 Midmean - Empirical Distribution Function - Interpolation 0.986829268292683 Midmean - Closest Observation 0.97953488372093 Midmean - True Basic - Statistics Graphics Toolkit 0.97953488372093 Midmean - MS Excel (old versions) 0.97953488372093 Number of observations 75

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/05/t12495076775km8f6b59rjqe4i/17eyq1249507575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/05/t12495076775km8f6b59rjqe4i/17eyq1249507575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/05/t12495076775km8f6b59rjqe4i/2wh2h1249507575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/05/t12495076775km8f6b59rjqe4i/2wh2h1249507575.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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