part 2.1

*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: Wed, 21 Oct 2009 11:37:12 -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/21/t1256147418v8ah5mbh74p8u28.htm/, Retrieved Wed, 21 Oct 2009 19:50:20 +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/21/t1256147418v8ah5mbh74p8u28.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 «

2.1 1.9 1 0.2 0.2 0.5 0.6 0.5 0.1 -0.1 0 1.1 1.3 1.2 0.6 0.2 0.3 0.4 0.4 0.2 0 0 0 0.8 1 0.8 0.3 0 0 0.1 0.1 0.1 0.2 -0.2 -0.7 -0.6 -0.9 -1.3 -1.1 -1.1 -1 -1.1 -1.4 -1.9 -2.2 -2.5 -2.1 -0.8 -0.3 -0.7 -1.1 -1.5 -1.2 -0.7 -0.6 -0.8 -1.3 -1.8 -1.7 -0.9 -0.5

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.260655737704918 0.127014449686231 -2.0521738931974 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 1.0177925325646 Winsorized Mean ( 1 / 20 ) -0.259016393442623 0.124671744932811 -2.07758697515795 Winsorized Mean ( 2 / 20 ) -0.275409836065574 0.118797613122627 -2.31831119183586 Winsorized Mean ( 3 / 20 ) -0.270491803278689 0.115312458918975 -2.34572921100183 Winsorized Mean ( 4 / 20 ) -0.270491803278689 0.112433204512823 -2.40579999877028 Winsorized Mean ( 5 / 20 ) -0.270491803278689 0.108977970960272 -2.48207780797549 Winsorized Mean ( 6 / 20 ) -0.250819672131148 0.104871061890139 -2.39169574151829 Winsorized Mean ( 7 / 20 ) -0.262295081967213 0.0982681714567581 -2.66917637805679 Winsorized Mean ( 8 / 20 ) -0.249180327868852 0.0958032749482912 -2.6009583493189 Winsorized Mean ( 9 / 20 ) -0.278688524590164 0.0907200929689617 -3.07196030636248 Winsorized Mean ( 10 / 20 ) -0.262295081967213 0.0877204929738486 -2.99012320924153 Winsorized Mean ( 11 / 20 ) -0.262295081967213 0.0816885975156739 -3.21091425173367 Winsorized Mean ( 12 / 20 ) -0.262295081967213 0.0816885975156739 -3.21091425173367 Winsorized Mean ( 13 / 20 ) -0.283606557377049 0.0784821976217896 -3.61364189550051 Winsorized Mean ( 14 / 20 ) -0.283606557377049 0.0784821976217896 -3.61364189550051 Winsorized Mean ( 15 / 20 ) -0.283606557377049 0.0707948752378241 -4.00603230706062 Winsorized Mean ( 16 / 20 ) -0.257377049180328 0.0664665993770635 -3.8722764755909 Winsorized Mean ( 17 / 20 ) -0.285245901639344 0.0627178635874296 -4.54808064757671 Winsorized Mean ( 18 / 20 ) -0.255737704918033 0.0579958821867777 -4.40958384070133 Winsorized Mean ( 19 / 20 ) -0.255737704918033 0.0579958821867777 -4.40958384070133 Winsorized Mean ( 20 / 20 ) -0.222950819672131 0.0529662972862258 -4.2092959314736 Trimmed Mean ( 1 / 20 ) -0.262711864406780 0.118998801743515 -2.20768495613105 Trimmed Mean ( 2 / 20 ) -0.266666666666667 0.111980723964808 -2.38136223115035 Trimmed Mean ( 3 / 20 ) -0.261818181818182 0.107324076051348 -2.4395102334067 Trimmed Mean ( 4 / 20 ) -0.258490566037736 0.103264352884541 -2.50319261988455 Trimmed Mean ( 5 / 20 ) -0.254901960784314 0.0993434812091193 -2.56586499367525 Trimmed Mean ( 6 / 20 ) -0.251020408163265 0.0956148403513006 -2.62532894727415 Trimmed Mean ( 7 / 20 ) -0.251063829787234 0.0921965653613843 -2.72313647263469 Trimmed Mean ( 8 / 20 ) -0.248888888888889 0.0897596241272032 -2.77283791358323 Trimmed Mean ( 9 / 20 ) -0.248837209302326 0.0872473154510423 -2.85209015332921 Trimmed Mean ( 10 / 20 ) -0.24390243902439 0.0852577712993041 -2.86076489342129 Trimmed Mean ( 11 / 20 ) -0.241025641025641 0.0833442326517054 -2.89192945159006 Trimmed Mean ( 12 / 20 ) -0.237837837837838 0.082231577283747 -2.89229327338765 Trimmed Mean ( 13 / 20 ) -0.234285714285714 0.080538404341218 -2.90899374282501 Trimmed Mean ( 14 / 20 ) -0.227272727272727 0.0788497717268567 -2.88235111269595 Trimmed Mean ( 15 / 20 ) -0.219354838709677 0.0762592289269397 -2.87643662014772 Trimmed Mean ( 16 / 20 ) -0.210344827586207 0.0746658941776957 -2.81714737234127 Trimmed Mean ( 17 / 20 ) -0.203703703703704 0.0734733475876812 -2.77248431426932 Trimmed Mean ( 18 / 20 ) -0.192 0.0723233480050991 -2.65474435705691 Trimmed Mean ( 19 / 20 ) -0.182608695652174 0.0718617947588988 -2.54110958771401 Trimmed Mean ( 20 / 20 ) -0.171428571428571 0.0704214716792357 -2.43432247780074 Median 0 Midrange -0.2 Midmean - Weighted Average at Xnp -0.219354838709677 Midmean - Weighted Average at X(n+1)p -0.219354838709677 Midmean - Empirical Distribution Function -0.219354838709677 Midmean - Empirical Distribution Function - Averaging -0.219354838709677 Midmean - Empirical Distribution Function - Interpolation -0.219354838709677 Midmean - Closest Observation -0.32 Midmean - True Basic - Statistics Graphics Toolkit -0.219354838709677 Midmean - MS Excel (old versions) -0.219354838709677 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256147418v8ah5mbh74p8u28/1k9qs1256146630.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256147418v8ah5mbh74p8u28/1k9qs1256146630.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256147418v8ah5mbh74p8u28/2hsy51256146630.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256147418v8ah5mbh74p8u28/2hsy51256146630.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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