Nicolas Van hoeij central tendency

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 23 Jan 2010 06:50:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/23/t1264254720s2ntkt3q1yor4yl.htm/, Retrieved Sat, 23 Jan 2010 14:52:02 +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/2010/Jan/23/t1264254720s2ntkt3q1yor4yl.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

Verbetering benoeming grafiek

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

1 4 -3 -3 0 6 -1 0 -1 1 -4 -1 -1 0 3 0 8 8 8 8 11 13 5 12 13 9 11 7 12 11 10 13 14 10 13 12 13 17 15 6 9 6 11 12 13 11 16 16 19 14 15 12 14 16 13 13 15 12 13 12 15 10 8 11 8 13 9 8 8 6 8 6 12 16

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 8.91891891891892 0.649881587698219 13.7239138448411 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 10.5061114775343 Winsorized Mean ( 1 / 24 ) 8.9054054054054 0.641109540959586 13.890614374692 Winsorized Mean ( 2 / 24 ) 8.87837837837838 0.636700788733181 13.9443495838027 Winsorized Mean ( 3 / 24 ) 8.95945945945946 0.617359387671828 14.5125507741077 Winsorized Mean ( 4 / 24 ) 8.95945945945946 0.617359387671828 14.5125507741077 Winsorized Mean ( 5 / 24 ) 8.95945945945946 0.617359387671828 14.5125507741077 Winsorized Mean ( 6 / 24 ) 8.87837837837838 0.605403504651377 14.6652246149302 Winsorized Mean ( 7 / 24 ) 8.97297297297297 0.5848807689382 15.3415421561263 Winsorized Mean ( 8 / 24 ) 8.97297297297297 0.5848807689382 15.3415421561263 Winsorized Mean ( 9 / 24 ) 8.97297297297297 0.5848807689382 15.3415421561263 Winsorized Mean ( 10 / 24 ) 8.83783783783784 0.566897225829101 15.5898413948177 Winsorized Mean ( 11 / 24 ) 8.98648648648649 0.535829619776941 16.7711641066566 Winsorized Mean ( 12 / 24 ) 8.98648648648649 0.535829619776941 16.7711641066566 Winsorized Mean ( 13 / 24 ) 9.16216216216216 0.444651054393115 20.6052860364116 Winsorized Mean ( 14 / 24 ) 9.35135135135135 0.409726447437665 22.8234018326924 Winsorized Mean ( 15 / 24 ) 9.55405405405405 0.374661091772583 25.5005237102478 Winsorized Mean ( 16 / 24 ) 9.77027027027027 0.3401696645829 28.7217564865760 Winsorized Mean ( 17 / 24 ) 9.77027027027027 0.3401696645829 28.7217564865760 Winsorized Mean ( 18 / 24 ) 9.77027027027027 0.3401696645829 28.7217564865760 Winsorized Mean ( 19 / 24 ) 9.77027027027027 0.3401696645829 28.7217564865760 Winsorized Mean ( 20 / 24 ) 9.77027027027027 0.3401696645829 28.7217564865760 Winsorized Mean ( 21 / 24 ) 10.0540540540541 0.298640565392576 33.6660695804589 Winsorized Mean ( 22 / 24 ) 10.3513513513514 0.259176230701608 39.9394316497679 Winsorized Mean ( 23 / 24 ) 10.0405405405405 0.218065260985262 46.0437416541056 Winsorized Mean ( 24 / 24 ) 10.0405405405405 0.218065260985262 46.0437416541056 Trimmed Mean ( 1 / 24 ) 8.95833333333333 0.627498916695347 14.2762530659199 Trimmed Mean ( 2 / 24 ) 9.01428571428571 0.611312560345332 14.7457884869788 Trimmed Mean ( 3 / 24 ) 9.08823529411765 0.594729298584008 15.2812974167505 Trimmed Mean ( 4 / 24 ) 9.13636363636364 0.583729015440244 15.6517209093556 Trimmed Mean ( 5 / 24 ) 9.1875 0.570381294774444 16.1076460328756 Trimmed Mean ( 6 / 24 ) 9.24193548387097 0.554146660505145 16.6777789032352 Trimmed Mean ( 7 / 24 ) 9.31666666666667 0.537567058839666 17.3311710854765 Trimmed Mean ( 8 / 24 ) 9.37931034482759 0.522817293794111 17.9399389732529 Trimmed Mean ( 9 / 24 ) 9.44642857142857 0.504473264487386 18.7253304315887 Trimmed Mean ( 10 / 24 ) 9.51851851851852 0.481481481481482 19.7692307692308 Trimmed Mean ( 11 / 24 ) 9.61538461538461 0.456356022334041 21.0699194155619 Trimmed Mean ( 12 / 24 ) 9.7 0.432600112277906 22.4225554379159 Trimmed Mean ( 13 / 24 ) 9.79166666666667 0.401634882942477 24.3795225029521 Trimmed Mean ( 14 / 24 ) 9.8695652173913 0.385245634235811 25.6188891977166 Trimmed Mean ( 15 / 24 ) 9.93181818181818 0.372690530855497 26.6489684055564 Trimmed Mean ( 16 / 24 ) 9.97619047619048 0.364651991093844 27.3581132692158 Trimmed Mean ( 17 / 24 ) 10 0.361620285339790 27.6533159377486 Trimmed Mean ( 18 / 24 ) 10.0263157894737 0.35678117280855 28.1021437049141 Trimmed Mean ( 19 / 24 ) 10.0555555555556 0.349476807242921 28.7731699132926 Trimmed Mean ( 20 / 24 ) 10.0882352941176 0.338729004937253 29.7826142641266 Trimmed Mean ( 21 / 24 ) 10.125 0.323008788455291 31.3458963405308 Trimmed Mean ( 22 / 24 ) 10.1333333333333 0.313428696664361 32.3305856840056 Trimmed Mean ( 23 / 24 ) 10.1071428571429 0.310057537390755 32.5976363683918 Trimmed Mean ( 24 / 24 ) 10.1153846153846 0.315384615384615 32.0731707317073 Median 10.5 Midrange 7.5 Midmean - Weighted Average at Xnp 10.1777777777778 Midmean - Weighted Average at X(n+1)p 10.1777777777778 Midmean - Empirical Distribution Function 10.1777777777778 Midmean - Empirical Distribution Function - Averaging 10.1777777777778 Midmean - Empirical Distribution Function - Interpolation 10.1777777777778 Midmean - Closest Observation 10.1777777777778 Midmean - True Basic - Statistics Graphics Toolkit 10.1777777777778 Midmean - MS Excel (old versions) 10.1777777777778 Number of observations 74

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/23/t1264254720s2ntkt3q1yor4yl/1gdsu1264254612.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264254720s2ntkt3q1yor4yl/1gdsu1264254612.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264254720s2ntkt3q1yor4yl/2swn11264254612.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264254720s2ntkt3q1yor4yl/2swn11264254612.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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