Shw3: Part 2

*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: Thu, 15 Oct 2009 11:00:13 -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/15/t12556260587tk9qry1y4s5s7k.htm/, Retrieved Thu, 15 Oct 2009 19:01:00 +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/Oct/15/t12556260587tk9qry1y4s5s7k.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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No (this computation is public)

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Dataseries X:

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26442.90 24863.62 25152.29 27539.80 27920.04 26945.05 26129.44 25406.62 25663.17 26066.60 26306.23 27105.07 27239.67 26296.19 25873.03 25917.65 25853.93 24803.73 23821.36 22950.51 22765.47 24710.92 23983.59 24434.12 23939.23 24290.02 24117.63 23724.64 22989.44 23716.86 25058.83 25059.00 23579.18 24209.03 24173.67 24706.39 24522.12 24766.15 25940.04 24985.78 24788.00 26544.56 28019.08 27285.71 29161.16 28357.73 27979.91 27543.95 27397.53 27623.59 27736.07 27803.79 27779.55 27524.13 27582.72 28638.95 28825.78 30132.61 29326.85 29075.62 28230.63 28118.36 28173.29 27396.91 24578.55 24504.77 27582.37 26920.31 25426.68 25390.80 25041.16 22769.42 22921.89 26267.63 27364.67 28382.59 29132.81 28214.51 28865.73 24405.35

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 26159.809125 208.435470317083 125.505553758217 Geometric Mean 26093.9918962458 Harmonic Mean 26028.0496767391 Quadratic Mean 26225.3273713418 Winsorized Mean ( 1 / 26 ) 26149.7865 206.226934806736 126.801023952114 Winsorized Mean ( 2 / 26 ) 26149.456 204.661224665933 127.769468997772 Winsorized Mean ( 3 / 26 ) 26149.466125 204.250416652542 128.026500770786 Winsorized Mean ( 4 / 26 ) 26148.553125 203.341191795411 128.594471656825 Winsorized Mean ( 5 / 26 ) 26172.29375 194.243525454418 134.739593964699 Winsorized Mean ( 6 / 26 ) 26179.6235 192.008289774734 136.346318852765 Winsorized Mean ( 7 / 26 ) 26163.956625 189.116927037112 138.348042319161 Winsorized Mean ( 8 / 26 ) 26147.992625 183.448693398228 142.535725606059 Winsorized Mean ( 9 / 26 ) 26158.45625 180.923796924878 144.582728721205 Winsorized Mean ( 10 / 26 ) 26148.11375 177.664360374261 147.177034802688 Winsorized Mean ( 11 / 26 ) 26164.32775 174.545715122684 149.899570617415 Winsorized Mean ( 12 / 26 ) 26166.55075 172.391579732179 151.785550028902 Winsorized Mean ( 13 / 26 ) 26163.370625 170.247253748306 153.678664700695 Winsorized Mean ( 14 / 26 ) 26160.169875 165.708219829513 157.868872780811 Winsorized Mean ( 15 / 26 ) 26174.449875 161.624228383279 161.946325354942 Winsorized Mean ( 16 / 26 ) 26168.229875 159.147916308583 164.427097017473 Winsorized Mean ( 17 / 26 ) 26158.539875 153.694420469943 170.198370214198 Winsorized Mean ( 18 / 26 ) 26156.989625 152.42658954763 171.603850106654 Winsorized Mean ( 19 / 26 ) 26160.06525 149.231744679310 175.298260475453 Winsorized Mean ( 20 / 26 ) 26163.90525 141.280221252821 185.191564806369 Winsorized Mean ( 21 / 26 ) 26154.366 139.729141428871 187.179036044631 Winsorized Mean ( 22 / 26 ) 26169.458 137.744200681916 189.985914981869 Winsorized Mean ( 23 / 26 ) 26164.694125 135.506481079260 193.088138047772 Winsorized Mean ( 24 / 26 ) 26168.168125 134.740174175362 194.212069897896 Winsorized Mean ( 25 / 26 ) 26181.986875 131.723668332876 198.764483303305 Winsorized Mean ( 26 / 26 ) 26180.543875 121.471316044171 215.528609778788 Trimmed Mean ( 1 / 26 ) 26152.3929487179 202.903338545913 128.890895222013 Trimmed Mean ( 2 / 26 ) 26155.1365789474 199.007780732361 131.427708417705 Trimmed Mean ( 3 / 26 ) 26158.2071621622 195.399037201098 133.870706513467 Trimmed Mean ( 4 / 26 ) 26161.4445833333 191.318962019772 136.742559687469 Trimmed Mean ( 5 / 26 ) 26165.1278571429 186.811136187654 140.06192773679 Trimmed Mean ( 6 / 26 ) 26163.4417647059 184.197177999222 142.040405009985 Trimmed Mean ( 7 / 26 ) 26160.1727272727 181.616794004064 144.040494001273 Trimmed Mean ( 8 / 26 ) 26159.49703125 179.165285961136 146.007620231323 Trimmed Mean ( 9 / 26 ) 26161.3525806452 177.397280047397 147.473245213542 Trimmed Mean ( 10 / 26 ) 26161.7816666667 175.680156048320 148.917113094270 Trimmed Mean ( 11 / 26 ) 26163.6668965517 174.121242371577 150.261200415272 Trimmed Mean ( 12 / 26 ) 26163.5810714286 172.679200784433 151.515532574709 Trimmed Mean ( 13 / 26 ) 26163.2144444444 171.15659128336 152.861273108260 Trimmed Mean ( 14 / 26 ) 26163.1959615385 169.507819764107 154.348017678170 Trimmed Mean ( 15 / 26 ) 26163.5418 168.118706387612 155.625405180538 Trimmed Mean ( 16 / 26 ) 26162.3297916667 166.918317906668 156.737319904549 Trimmed Mean ( 17 / 26 ) 26161.6884782609 165.619577608285 157.962535927590 Trimmed Mean ( 18 / 26 ) 26162.0252272727 164.724603356963 158.822815135750 Trimmed Mean ( 19 / 26 ) 26162.5580952381 163.498712246964 160.016906162048 Trimmed Mean ( 20 / 26 ) 26162.8205 162.210660084724 161.289156251106 Trimmed Mean ( 21 / 26 ) 26162.7063157895 161.765128883884 161.732670670755 Trimmed Mean ( 22 / 26 ) 26163.5888888889 161.018575833033 162.488015767939 Trimmed Mean ( 23 / 26 ) 26162.9611764706 159.941523225370 163.578291921136 Trimmed Mean ( 24 / 26 ) 26162.7728125 158.446842975931 165.120189971058 Trimmed Mean ( 25 / 26 ) 26162.1733333333 155.959568920947 167.749715611194 Trimmed Mean ( 26 / 26 ) 26159.9089285714 152.666062407256 171.35379347629 Median 26098.02 Midrange 26449.04 Midmean - Weighted Average at Xnp 26124.1797560976 Midmean - Weighted Average at X(n+1)p 26162.8205 Midmean - Empirical Distribution Function 26124.1797560976 Midmean - Empirical Distribution Function - Averaging 26162.8205 Midmean - Empirical Distribution Function - Interpolation 26162.8205 Midmean - Closest Observation 26124.1797560976 Midmean - True Basic - Statistics Graphics Toolkit 26162.8205 Midmean - MS Excel (old versions) 26162.5580952381 Number of observations 80

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/15/t12556260587tk9qry1y4s5s7k/13k3d1255626011.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/15/t12556260587tk9qry1y4s5s7k/13k3d1255626011.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/15/t12556260587tk9qry1y4s5s7k/23yq81255626012.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/15/t12556260587tk9qry1y4s5s7k/23yq81255626012.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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