Investigating distributions Q6

*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: Sun, 26 Oct 2008 09:28:26 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/26/t1225035034snyv4iuntzns3t8.htm/, Retrieved Sun, 26 Oct 2008 15:30:36 +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/Oct/26/t1225035034snyv4iuntzns3t8.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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0,127030435 0,056987137 0,063317076 0,063512053 0,204566667 -0,010991235 0,168593069 0,126931079 0,050900978 -0,069376736 0,116070478 0,125413007 0,047333962 0,021508147 -0,03464902 -0,0368851 0,161155814 -0,046681976 0,164092703 0,052642451 -0,054823697 -0,122969565 0,12763306 0,110064948 -0,008210057 -0,005235346 -0,086360958 -0,072626316 0,069250114 -0,12238921 0,023145902 -0,019664906 -0,043641582 -0,13454582 0,061138696 0,060580412 0,021662201 -0,043829835 -0,091052772 -0,036247217 0,062385126 -0,106934711 0,012571341 -0,046143518 -0,062292493 -0,149501575 -0,029119027 0,048223253 0,007049952 -0,082917121 -0,111845158 -0,10353986 0,058789988 -0,118108359 -0,045845583 -0,092506043 -0,078092647 -0,178815543 -0,011594949 0,038595134 0,006298268

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 9.0426229508886e-08 0.0114291533021248 7.91189225645219e-06 Geometric Mean NaN Harmonic Mean -0.440992738643873 Quadratic Mean 0.0885298408008078 Winsorized Mean ( 1 / 20 ) -0.000109083836065573 0.0111502480278886 -0.00978308606164966 Winsorized Mean ( 2 / 20 ) 0.000233715803278689 0.0110085322801376 0.0212304235779347 Winsorized Mean ( 3 / 20 ) 0.000658602655737705 0.0108607091364145 0.0606408520351126 Winsorized Mean ( 4 / 20 ) -0.00150155465573771 0.0103531978250052 -0.145032933893249 Winsorized Mean ( 5 / 20 ) -0.00120006072131148 0.0102755125989696 -0.116788404447270 Winsorized Mean ( 6 / 20 ) -0.000593780885245901 0.0101588317676167 -0.0584497212699887 Winsorized Mean ( 7 / 20 ) -0.000204491950819673 0.0100209628685834 -0.0204064173773933 Winsorized Mean ( 8 / 20 ) -0.000984515295081966 0.00969077564784127 -0.101593033505143 Winsorized Mean ( 9 / 20 ) -0.000242636885245903 0.00923404695015402 -0.0262763322036018 Winsorized Mean ( 10 / 20 ) -0.00669535213114754 0.00798724816389706 -0.838255177973687 Winsorized Mean ( 11 / 20 ) -0.00688401962295082 0.00767868173199379 -0.896510607317927 Winsorized Mean ( 12 / 20 ) -0.00624489962295082 0.00755708675194955 -0.82636336301681 Winsorized Mean ( 13 / 20 ) -0.00541534532786885 0.00735497059804504 -0.736283749293064 Winsorized Mean ( 14 / 20 ) -0.00444684345901639 0.00710734829977794 -0.62566843096114 Winsorized Mean ( 15 / 20 ) -0.00378504936065574 0.00695956233210063 -0.543863131047392 Winsorized Mean ( 16 / 20 ) -0.00239650667213115 0.00660049543348655 -0.363079816701767 Winsorized Mean ( 17 / 20 ) -0.000817472819672131 0.00621439653638094 -0.131545004392044 Winsorized Mean ( 18 / 20 ) 0.000302963737704918 0.00567639224490088 0.053372586782929 Winsorized Mean ( 19 / 20 ) -7.17458524590179e-05 0.00557021747750842 -0.0128802605551247 Winsorized Mean ( 20 / 20 ) -0.00085200486885246 0.00542357106444244 -0.157092966742577 Trimmed Mean ( 1 / 20 ) -0.000436366237288135 0.0108689626323786 -0.0401479195436923 Trimmed Mean ( 2 / 20 ) -0.000786615824561403 0.0105229395313002 -0.0747524797820645 Trimmed Mean ( 3 / 20 ) -0.00135243609090909 0.0101895014217329 -0.132728387281493 Trimmed Mean ( 4 / 20 ) -0.00212396667924528 0.00984516991178467 -0.215736924631732 Trimmed Mean ( 5 / 20 ) -0.00231008007843137 0.00961676338850195 -0.240213883310612 Trimmed Mean ( 6 / 20 ) -0.00258645224489796 0.00935158638958732 -0.276578982126272 Trimmed Mean ( 7 / 20 ) -0.00301749108510638 0.00904727309070538 -0.333524925671401 Trimmed Mean ( 8 / 20 ) -0.0035622306 0.00869401211366102 -0.409733797633272 Trimmed Mean ( 9 / 20 ) -0.00401932546511628 0.00833090155268804 -0.482459844195303 Trimmed Mean ( 10 / 20 ) -0.00464365609756098 0.0079817772173857 -0.581782223568742 Trimmed Mean ( 11 / 20 ) -0.00432274979487179 0.00785974978204419 -0.549985675720521 Trimmed Mean ( 12 / 20 ) -0.00393887397297297 0.00776021353221818 -0.507572885284651 Trimmed Mean ( 13 / 20 ) -0.0036039512 0.00763942698591083 -0.471756743882317 Trimmed Mean ( 14 / 20 ) -0.003346387 0.00750909119782298 -0.445644740733762 Trimmed Mean ( 15 / 20 ) -0.00319171454838710 0.00737514831120705 -0.432766151093811 Trimmed Mean ( 16 / 20 ) -0.00310851127586207 0.00720373584145335 -0.431513778999832 Trimmed Mean ( 17 / 20 ) -0.00320904896296296 0.00704112188384609 -0.455758189660832 Trimmed Mean ( 18 / 20 ) -0.00355231048 0.00689356397359014 -0.515308263419215 Trimmed Mean ( 19 / 20 ) -0.00412035813043478 0.00681304458128153 -0.604774866989017 Trimmed Mean ( 20 / 20 ) -0.00473931890476190 0.0066701101111457 -0.7105308346923 Median -0.008210057 Midrange 0.012875562 Midmean - Weighted Average at Xnp -0.0053174521 Midmean - Weighted Average at X(n+1)p -0.00319171454838709 Midmean - Empirical Distribution Function -0.00319171454838709 Midmean - Empirical Distribution Function - Averaging -0.00319171454838709 Midmean - Empirical Distribution Function - Interpolation -0.00319171454838709 Midmean - Closest Observation -0.00536154584375 Midmean - True Basic - Statistics Graphics Toolkit -0.00319171454838709 Midmean - MS Excel (old versions) -0.00319171454838709 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225035034snyv4iuntzns3t8/13juu1225034903.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225035034snyv4iuntzns3t8/13juu1225034903.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225035034snyv4iuntzns3t8/2q6pb1225034903.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225035034snyv4iuntzns3t8/2q6pb1225034903.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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