WS3 Q2 Central Tendency e(t)

*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, 22 Oct 2009 14:08:54 -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/22/t1256242285huujq84bbilfc21.htm/, Retrieved Thu, 22 Oct 2009 22:11:28 +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/22/t1256242285huujq84bbilfc21.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:

KVN WS3

Dataseries X:

» Textbox « » Textfile « » CSV «

7,06 2,98 3,22 2,27 1,07 0,58 1,17 0,44 0,97 2,12 3,52 3,39 6,02 2,79 2,67 2,07 0,85 0,80 1,15 0,45 0,95 1,93 3,52 3,23 5,02 2,60 3,29 1,49 0,88 0,91 0,73 0,78 0,91 1,93 3,60 3,29 5,08 3,23 3,59 1,64 1,03 0,97 0,66 0,81 0,83 2,23 3,57 3,20 5,64 3,52 3,13 1,71 1,18 0,75 0,79 0,77 0,65 2,48 3,98 2,69

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.24633333333333 0.198160747204334 11.3359147309685 Geometric Mean 1.75992811634205 Harmonic Mean 1.3675618812354 Quadratic Mean 2.71344921947448 Winsorized Mean ( 1 / 20 ) 2.22916666666667 0.191649882586168 11.6314533386912 Winsorized Mean ( 2 / 20 ) 2.22083333333333 0.18689724837486 11.8826432847155 Winsorized Mean ( 3 / 20 ) 2.19633333333333 0.178186242734426 12.3260544676663 Winsorized Mean ( 4 / 20 ) 2.193 0.176998244429354 12.3899533979576 Winsorized Mean ( 5 / 20 ) 2.11216666666667 0.155382722622698 13.5933173972981 Winsorized Mean ( 6 / 20 ) 2.07616666666667 0.147876703044129 14.0398495768945 Winsorized Mean ( 7 / 20 ) 2.07733333333333 0.147320486696103 14.1007770196858 Winsorized Mean ( 8 / 20 ) 2.076 0.146658101958455 14.1553720679413 Winsorized Mean ( 9 / 20 ) 2.07 0.145151197227226 14.2609915697735 Winsorized Mean ( 10 / 20 ) 2.07166666666667 0.144902688302229 14.2969512225040 Winsorized Mean ( 11 / 20 ) 2.0735 0.144630607797466 14.3365227566743 Winsorized Mean ( 12 / 20 ) 2.0515 0.139722045504638 14.6827223477193 Winsorized Mean ( 13 / 20 ) 2.03416666666667 0.135620209913935 14.9989936452506 Winsorized Mean ( 14 / 20 ) 2.04116666666667 0.134590421093383 15.1657647705140 Winsorized Mean ( 15 / 20 ) 2.03366666666667 0.131158240276648 15.5054433665556 Winsorized Mean ( 16 / 20 ) 2.03366666666667 0.131158240276648 15.5054433665556 Winsorized Mean ( 17 / 20 ) 2.04216666666667 0.129084584818114 15.8203759925647 Winsorized Mean ( 18 / 20 ) 2.04216666666667 0.127299657968986 16.0422007352463 Winsorized Mean ( 19 / 20 ) 2.02 0.123907884502189 16.3024331188893 Winsorized Mean ( 20 / 20 ) 1.99 0.113543590275521 17.5263085760379 Trimmed Mean ( 1 / 20 ) 2.19448275862069 0.184401907980628 11.9005425846853 Trimmed Mean ( 2 / 20 ) 2.15732142857143 0.175312613371758 12.3055688183527 Trimmed Mean ( 3 / 20 ) 2.12203703703704 0.167167043341171 12.6941111993359 Trimmed Mean ( 4 / 20 ) 2.09346153846154 0.161323682901210 12.9767774998263 Trimmed Mean ( 5 / 20 ) 2.0636 0.154332204635828 13.3711561036104 Trimmed Mean ( 6 / 20 ) 2.05145833333333 0.153124951753744 13.3972831327483 Trimmed Mean ( 7 / 20 ) 2.04608695652174 0.153547260426961 13.3254540057067 Trimmed Mean ( 8 / 20 ) 2.04 0.153861844621868 13.2586477499572 Trimmed Mean ( 9 / 20 ) 2.03357142857143 0.154039612621275 13.2016134938694 Trimmed Mean ( 10 / 20 ) 2.0275 0.154219602831274 13.1468371256163 Trimmed Mean ( 11 / 20 ) 2.02052631578947 0.154050086702821 13.1160349145878 Trimmed Mean ( 12 / 20 ) 2.0125 0.153401317744387 13.1191832612119 Trimmed Mean ( 13 / 20 ) 2.00676470588235 0.153257394542189 13.0940807905352 Trimmed Mean ( 14 / 20 ) 2.0028125 0.153481265520999 13.0492310784731 Trimmed Mean ( 15 / 20 ) 1.99733333333333 0.153314291671231 13.0277047988223 Trimmed Mean ( 16 / 20 ) 1.99214285714286 0.153215411127945 13.0022354962667 Trimmed Mean ( 17 / 20 ) 1.98615384615385 0.152127554701337 13.0558454716054 Trimmed Mean ( 18 / 20 ) 1.97791666666667 0.150152071666041 13.1727564243391 Trimmed Mean ( 19 / 20 ) 1.96818181818182 0.146634150808713 13.4223972200674 Trimmed Mean ( 20 / 20 ) 1.96 0.141292902194435 13.8718928520756 Median 2 Midrange 3.75 Midmean - Weighted Average at Xnp 1.96129032258065 Midmean - Weighted Average at X(n+1)p 1.99733333333333 Midmean - Empirical Distribution Function 1.96129032258065 Midmean - Empirical Distribution Function - Averaging 1.99733333333333 Midmean - Empirical Distribution Function - Interpolation 1.99733333333333 Midmean - Closest Observation 1.96129032258065 Midmean - True Basic - Statistics Graphics Toolkit 1.99733333333333 Midmean - MS Excel (old versions) 2.04181818181818 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/22/t1256242285huujq84bbilfc21/12h6g1256242130.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t1256242285huujq84bbilfc21/12h6g1256242130.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t1256242285huujq84bbilfc21/245ei1256242130.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t1256242285huujq84bbilfc21/245ei1256242130.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 36 ;

Parameters (R input):

par1 = 0 ; par2 = 36 ;

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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