central tendency na arima

*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: Fri, 24 Dec 2010 09:32:26 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293183060jac2v3i2658r8qh.htm/, Retrieved Fri, 24 Dec 2010 10:31:01 +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/Dec/24/t1293183060jac2v3i2658r8qh.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:

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Dataseries X:

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0.217499822516866 -9.78478953094158 -4.69092289728636 10.8303737739891 17.4025635868567 -18.695949344517 -1.45165150662704 24.2055636204555 -7.85142459641661 -9.4984274601968 15.4524605741829 -4.57316796503045 -35.3790647494429 -1.71841266886546 16.4887231604473 12.3672525241091 -30.5270631334762 14.0831320895415 12.2671755298376 7.6573009730872 -10.2588701804503 4.98218909929218 18.2374731745486 -18.1217207388952 19.2509327179740 20.7168346335646 27.0084172311441 -13.1935985382014 3.91871968362315 23.2274665865825 39.0004011190054 23.2030259046977 50.985499051697 26.9190549927636 5.61997889463015 -49.70729388275 -6.42398274476005 -41.6977425555609 -7.92694134412627 5.34208987982118 27.7759340629904 -6.52456657092852 3.12509229100933 -4.61574932357839 11.4276121576526 18.3833489895730 -42.4568062507692 7.51193809087255 -16.7513836179227 8.95264961600874 8.81854600123269 -18.5966360042492 11.7598212958319 etc...

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.42062875682102 2.5404507943611 0.952834340343832 Geometric Mean NaN Harmonic Mean 15.6671824563002 Quadratic Mean 19.8265694938016 Winsorized Mean ( 1 / 20 ) 2.34301219451428 2.44597739146852 0.957904272822237 Winsorized Mean ( 2 / 20 ) 1.99988421547144 2.35863448115861 0.847899168543086 Winsorized Mean ( 3 / 20 ) 2.21946610009744 2.27552690727673 0.975363592933127 Winsorized Mean ( 4 / 20 ) 2.28484099070919 2.25445140919332 1.01347981215827 Winsorized Mean ( 5 / 20 ) 2.46012871559924 2.10768092769793 1.16722065625287 Winsorized Mean ( 6 / 20 ) 3.52763856036182 1.81797582371867 1.94042105199509 Winsorized Mean ( 7 / 20 ) 3.53623050476643 1.81515032469934 1.94817501153915 Winsorized Mean ( 8 / 20 ) 3.27245660236917 1.74582747712578 1.87444443694788 Winsorized Mean ( 9 / 20 ) 3.25835687857305 1.66969043625669 1.95147364314911 Winsorized Mean ( 10 / 20 ) 3.69937349354359 1.53506609312419 2.40991154069111 Winsorized Mean ( 11 / 20 ) 4.20228132911726 1.43780610518944 2.92270377344348 Winsorized Mean ( 12 / 20 ) 4.24485005009673 1.41405050593166 3.00190837052172 Winsorized Mean ( 13 / 20 ) 4.2088987041472 1.38838175749079 3.03151397764971 Winsorized Mean ( 14 / 20 ) 4.54153021864797 1.32590538254621 3.4252294910566 Winsorized Mean ( 15 / 20 ) 4.33538505175459 1.28713223271694 3.36825148306887 Winsorized Mean ( 16 / 20 ) 4.17843262239513 1.2268099460256 3.40593311615354 Winsorized Mean ( 17 / 20 ) 4.04456405773544 1.13048785814642 3.57771561064531 Winsorized Mean ( 18 / 20 ) 3.56791941336248 1.05302583181198 3.38825440513936 Winsorized Mean ( 19 / 20 ) 4.07655341681889 0.96501973384413 4.22432130022881 Winsorized Mean ( 20 / 20 ) 3.9348548396721 0.937948307958956 4.19517238453644 Trimmed Mean ( 1 / 20 ) 2.48101947452771 2.32795855718086 1.06574898718653 Trimmed Mean ( 2 / 20 ) 2.6287114759456 2.18152123515123 1.20499009296298 Trimmed Mean ( 3 / 20 ) 2.97742477493581 2.05864638072713 1.44630219294105 Trimmed Mean ( 4 / 20 ) 3.26821395207506 1.94716382875283 1.67844836875815 Trimmed Mean ( 5 / 20 ) 3.56226174934622 1.81408906146238 1.96366420206216 Trimmed Mean ( 6 / 20 ) 3.83667038223833 1.70033085960256 2.25642577770724 Trimmed Mean ( 7 / 20 ) 3.9035176912258 1.65419240378584 2.35977246799832 Trimmed Mean ( 8 / 20 ) 3.97464314638142 1.59497926634403 2.49197167026001 Trimmed Mean ( 9 / 20 ) 4.09915878354638 1.53724912726993 2.66655463374779 Trimmed Mean ( 10 / 20 ) 4.23815313640105 1.48215155975356 2.8594600251986 Trimmed Mean ( 11 / 20 ) 4.32242379848902 1.4459395964481 2.98935295022482 Trimmed Mean ( 12 / 20 ) 4.34043040937766 1.42168530799028 3.05301770017822 Trimmed Mean ( 13 / 20 ) 4.35431231870179 1.39225449373325 3.1275261371403 Trimmed Mean ( 14 / 20 ) 4.37498884664545 1.35585537227626 3.22673711083253 Trimmed Mean ( 15 / 20 ) 4.35158095795385 1.31991318831627 3.29686906417299 Trimmed Mean ( 16 / 20 ) 4.35385210801858 1.27692439143651 3.40963970710953 Trimmed Mean ( 17 / 20 ) 4.37862198909041 1.23015754511239 3.55939936838769 Trimmed Mean ( 18 / 20 ) 4.42656912747312 1.18968719625679 3.720784035838 Trimmed Mean ( 19 / 20 ) 4.55308514815126 1.14902975159414 3.96254765538874 Trimmed Mean ( 20 / 20 ) 4.62593837023466 1.11588739687542 4.14552434518723 Median 5.34208987982118 Midrange 0.639102584473498 Midmean - Weighted Average at Xnp 3.94700955120407 Midmean - Weighted Average at X(n+1)p 4.35158095795385 Midmean - Empirical Distribution Function 4.35158095795385 Midmean - Empirical Distribution Function - Averaging 4.35158095795385 Midmean - Empirical Distribution Function - Interpolation 4.35158095795385 Midmean - Closest Observation 3.96787713601385 Midmean - True Basic - Statistics Graphics Toolkit 4.35158095795385 Midmean - MS Excel (old versions) 4.35158095795385 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293183060jac2v3i2658r8qh/1312u1293183142.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293183060jac2v3i2658r8qh/1312u1293183142.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293183060jac2v3i2658r8qh/2312u1293183142.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293183060jac2v3i2658r8qh/2312u1293183142.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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