Waerlop Jeroen - Bananen

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 07 Nov 2008 08:35:47 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/07/t1226072227ni3zypbv8j5o2jw.htm/, Retrieved Fri, 07 Nov 2008 15:37:09 +0000

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/2008/Nov/07/t1226072227ni3zypbv8j5o2jw.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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1,83 1,89 1,9 2,01 2,04 2,04 2,03 2,04 1,87 1,85 1,82 1,79 1,88 2,01 1,9 1,96 1,94 1,92 1,79 1,77 1,74 1,75 1,86 1,84 1,77 1,98 1,94 1,85 1,84 1,82 1,83 1,91 1,85 1,81 1,83 1,79 1,8 1,82 1,88 2,01 1,97 1,92 1,98 2,02 1,9 1,94 1,96 1,84 1,87 1,84 2,07 2,08 2,14 2,15 2,05 2,05 1,95 2,02 2,02 1,88 1,96 1,93 2,03 2,1 1,95 2,07 2,09 2,01 1,92 1,99 2,11 2

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 1.93069444444444 0.0120904364566544 159.687737607009 Geometric Mean 1.92801440940248 Harmonic Mean 1.92534383598924 Quadratic Mean 1.93338038735843 Winsorized Mean ( 1 / 24 ) 1.93069444444444 0.0120255439995653 160.549447452376 Winsorized Mean ( 2 / 24 ) 1.93041666666667 0.0117209293096181 164.698260323316 Winsorized Mean ( 3 / 24 ) 1.93 0.0116330837913965 165.906137582141 Winsorized Mean ( 4 / 24 ) 1.93055555555556 0.0113157985189916 170.607098766865 Winsorized Mean ( 5 / 24 ) 1.92986111111111 0.0111812025347660 172.598707975332 Winsorized Mean ( 6 / 24 ) 1.92902777777778 0.0110273520413873 174.931186611061 Winsorized Mean ( 7 / 24 ) 1.93 0.0108590341581653 177.732197163112 Winsorized Mean ( 8 / 24 ) 1.92888888888889 0.0102883991135958 187.481926740178 Winsorized Mean ( 9 / 24 ) 1.93013888888889 0.0100905389912735 191.282040588526 Winsorized Mean ( 10 / 24 ) 1.92875 0.00986397608759525 195.534740035061 Winsorized Mean ( 11 / 24 ) 1.92875 0.00986397608759525 195.534740035061 Winsorized Mean ( 12 / 24 ) 1.93041666666667 0.00961186811224533 200.836782623698 Winsorized Mean ( 13 / 24 ) 1.92861111111111 0.00932860702673737 206.741596637460 Winsorized Mean ( 14 / 24 ) 1.92861111111111 0.00932860702673737 206.741596637460 Winsorized Mean ( 15 / 24 ) 1.92861111111111 0.0087104921972016 221.412414757769 Winsorized Mean ( 16 / 24 ) 1.92861111111111 0.0087104921972016 221.412414757769 Winsorized Mean ( 17 / 24 ) 1.92861111111111 0.0087104921972016 221.412414757769 Winsorized Mean ( 18 / 24 ) 1.92611111111111 0.00834870777898326 230.707692986912 Winsorized Mean ( 19 / 24 ) 1.92875 0.00797329634571475 241.901205771263 Winsorized Mean ( 20 / 24 ) 1.92875 0.00797329634571475 241.901205771263 Winsorized Mean ( 21 / 24 ) 1.92875 0.00797329634571475 241.901205771263 Winsorized Mean ( 22 / 24 ) 1.92875 0.00711777047217193 270.976706475821 Winsorized Mean ( 23 / 24 ) 1.92875 0.00624217036961646 308.987080741680 Winsorized Mean ( 24 / 24 ) 1.92541666666667 0.00579020779072572 332.529804845802 Trimmed Mean ( 1 / 24 ) 1.93028571428571 0.0117142857142857 164.780487804878 Trimmed Mean ( 2 / 24 ) 1.92985294117647 0.0113440346590948 170.120508194081 Trimmed Mean ( 3 / 24 ) 1.92954545454545 0.0110970119630156 173.879730956071 Trimmed Mean ( 4 / 24 ) 1.929375 0.0108399132947683 177.988047278125 Trimmed Mean ( 5 / 24 ) 1.92903225806452 0.0106447606610188 181.218941364145 Trimmed Mean ( 6 / 24 ) 1.92883333333333 0.0104478572578593 184.615207284000 Trimmed Mean ( 7 / 24 ) 1.92879310344828 0.0102482128824563 188.207751494910 Trimmed Mean ( 8 / 24 ) 1.92857142857143 0.010043504625264 192.021759388669 Trimmed Mean ( 9 / 24 ) 1.92851851851852 0.00992426741257352 194.323514103942 Trimmed Mean ( 10 / 24 ) 1.92826923076923 0.0098124230745893 196.513054534182 Trimmed Mean ( 11 / 24 ) 1.9282 0.0097129831059426 198.517796125918 Trimmed Mean ( 12 / 24 ) 1.928125 0.00957730885260342 201.322211664488 Trimmed Mean ( 13 / 24 ) 1.92782608695652 0.00944811942782992 204.043365632955 Trimmed Mean ( 14 / 24 ) 1.92772727272727 0.00933215834197123 206.568213063569 Trimmed Mean ( 15 / 24 ) 1.92761904761905 0.00916875928269014 210.237720086973 Trimmed Mean ( 16 / 24 ) 1.9275 0.0090776564240913 212.334539880204 Trimmed Mean ( 17 / 24 ) 1.92736842105263 0.00893857822750383 215.623600532147 Trimmed Mean ( 18 / 24 ) 1.92722222222222 0.00873427031606788 220.650627068049 Trimmed Mean ( 19 / 24 ) 1.92735294117647 0.0085312555632066 225.916680950072 Trimmed Mean ( 20 / 24 ) 1.9271875 0.00833079178313027 231.333053348245 Trimmed Mean ( 21 / 24 ) 1.927 0.00802510428907778 240.121490087382 Trimmed Mean ( 22 / 24 ) 1.92678571428571 0.00756022681395592 254.858189006834 Trimmed Mean ( 23 / 24 ) 1.92653846153846 0.00716706801316448 268.804266681967 Trimmed Mean ( 24 / 24 ) 1.92625 0.00688446318410763 279.796688352787 Median 1.925 Midrange 1.945 Midmean - Weighted Average at Xnp 1.92051282051282 Midmean - Weighted Average at X(n+1)p 1.92051282051282 Midmean - Empirical Distribution Function 1.92051282051282 Midmean - Empirical Distribution Function - Averaging 1.92051282051282 Midmean - Empirical Distribution Function - Interpolation 1.92051282051282 Midmean - Closest Observation 1.92051282051282 Midmean - True Basic - Statistics Graphics Toolkit 1.92051282051282 Midmean - MS Excel (old versions) 1.92761904761905 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226072227ni3zypbv8j5o2jw/1d3x61226072145.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226072227ni3zypbv8j5o2jw/1d3x61226072145.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226072227ni3zypbv8j5o2jw/2hoqx1226072145.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/07/t1226072227ni3zypbv8j5o2jw/2hoqx1226072145.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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