*Unverified author*

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 09:42:50 -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/t122503580099e83dum347eagk.htm/, Retrieved Sun, 26 Oct 2008 15:43:20 +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/t122503580099e83dum347eagk.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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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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1,6600 1,6700 1,6500 1,6600 1,6500 1,6400 1,6500 1,6400 1,6400 1,6400 1,6400 1,6300 1,6400 1,6400 1,6400 1,6500 1,6400 1,6400 1,6300 1,6200 1,6100 1,6100 1,6200 1,6100 1,6200 1,6200 1,6200 1,6200 1,6200 1,6400 1,6400 1,6300 1,6200 1,6200 1,6200 1,6000 1,6300 1,6500 1,6700 1,6600 1,6700 1,6600 1,6600 1,6700 1,6700 1,6600 1,6600 1,6700 1,6700 1,6700 1,6700 1,6700 1,6600 1,6500 1,6500 1,6500 1,6300 1,6200 1,6200 1,6200 1,5300 1,5200 1,5100 1,5300 1,5500 1,5600 1,5700 1,5800 1,5800 1,5800 1,5800 1,5800 1,5900 1,5700 1,5900 1,5700 1,5800 1,5800 1,5800 1,5700

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.6225 0.00439180767834206 369.437853119403 Geometric Mean 1.62202330645261 Harmonic Mean 1.62153937849147 Quadratic Mean 1.62296950063764 Winsorized Mean ( 1 / 26 ) 1.622625 0.00435288261101955 372.770218037178 Winsorized Mean ( 2 / 26 ) 1.622875 0.00428122834467404 379.06761082223 Winsorized Mean ( 3 / 26 ) 1.622875 0.00428122834467404 379.06761082223 Winsorized Mean ( 4 / 26 ) 1.623875 0.00402717725529552 403.229085053232 Winsorized Mean ( 5 / 26 ) 1.6245 0.00388888386577935 417.729110991193 Winsorized Mean ( 6 / 26 ) 1.62525 0.00373985970765099 434.575125017409 Winsorized Mean ( 7 / 26 ) 1.62525 0.00373985970765099 434.575125017409 Winsorized Mean ( 8 / 26 ) 1.62525 0.00373985970765099 434.575125017409 Winsorized Mean ( 9 / 26 ) 1.62525 0.00373985970765099 434.575125017409 Winsorized Mean ( 10 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 11 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 12 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 13 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 14 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 15 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 16 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 17 / 26 ) 1.62525 0.00333743155242 486.976279355158 Winsorized Mean ( 18 / 26 ) 1.62525 0.00267415549191453 607.761966315736 Winsorized Mean ( 19 / 26 ) 1.62525 0.00267415549191453 607.761966315735 Winsorized Mean ( 20 / 26 ) 1.62775 0.00227099905523114 716.755031778 Winsorized Mean ( 21 / 26 ) 1.630375 0.00188635800392908 864.297761402716 Winsorized Mean ( 22 / 26 ) 1.630375 0.00188635800392908 864.297761402716 Winsorized Mean ( 23 / 26 ) 1.630375 0.00188635800392908 864.297761402716 Winsorized Mean ( 24 / 26 ) 1.633375 0.00150887406676868 1082.51247468117 Winsorized Mean ( 25 / 26 ) 1.633375 0.00150887406676868 1082.51247468117 Winsorized Mean ( 26 / 26 ) 1.630125 0.00108927089190400 1496.52856063252 Trimmed Mean ( 1 / 26 ) 1.62333333333333 0.00421952814949939 384.719161910539 Trimmed Mean ( 2 / 26 ) 1.62407894736842 0.00406170663110422 399.851366647546 Trimmed Mean ( 3 / 26 ) 1.62472972972973 0.00392083345081346 414.383765623261 Trimmed Mean ( 4 / 26 ) 1.62541666666667 0.00375260733561832 433.143284467531 Trimmed Mean ( 5 / 26 ) 1.62585714285714 0.00364860708066842 445.610367713063 Trimmed Mean ( 6 / 26 ) 1.62617647058824 0.00356815869079557 455.746678190946 Trimmed Mean ( 7 / 26 ) 1.62636363636364 0.00351245777342402 463.027242254423 Trimmed Mean ( 8 / 26 ) 1.6265625 0.00344470745123633 472.19176752331 Trimmed Mean ( 9 / 26 ) 1.62677419354839 0.00336226449047079 483.832904329488 Trimmed Mean ( 10 / 26 ) 1.627 0.00326165879256184 498.825935965572 Trimmed Mean ( 11 / 26 ) 1.62724137931034 0.00322378771418822 504.760711181039 Trimmed Mean ( 12 / 26 ) 1.6275 0.00317508564154871 512.584598885388 Trimmed Mean ( 13 / 26 ) 1.62777777777778 0.00311290753765543 522.912344195029 Trimmed Mean ( 14 / 26 ) 1.62807692307692 0.00303372772126335 536.658880645667 Trimmed Mean ( 15 / 26 ) 1.6284 0.00293271483893858 555.253439024899 Trimmed Mean ( 16 / 26 ) 1.62875 0.00280300307547721 581.073211888184 Trimmed Mean ( 17 / 26 ) 1.62913043478261 0.00263433455478301 618.421996486624 Trimmed Mean ( 18 / 26 ) 1.62954545454545 0.00241021753543818 676.098912478122 Trimmed Mean ( 19 / 26 ) 1.63 0.00228614978429605 712.989153727698 Trimmed Mean ( 20 / 26 ) 1.6305 0.00211678275474107 770.272715208061 Trimmed Mean ( 21 / 26 ) 1.63078947368421 0.00200928070565225 811.628494264979 Trimmed Mean ( 22 / 26 ) 1.63083333333333 0.00196698948117359 829.101197002999 Trimmed Mean ( 23 / 26 ) 1.63088235294118 0.00190541245500184 855.920905030296 Trimmed Mean ( 24 / 26 ) 1.6309375 0.00181611152981022 898.038183905164 Trimmed Mean ( 25 / 26 ) 1.63066666666667 0.00178971090796798 911.134116357436 Trimmed Mean ( 26 / 26 ) 1.63035714285714 0.00174287232190457 935.44267263108 Median 1.63 Midrange 1.59 Midmean - Weighted Average at Xnp 1.62954545454546 Midmean - Weighted Average at X(n+1)p 1.63142857142857 Midmean - Empirical Distribution Function 1.62954545454546 Midmean - Empirical Distribution Function - Averaging 1.63142857142857 Midmean - Empirical Distribution Function - Interpolation 1.63142857142857 Midmean - Closest Observation 1.62954545454546 Midmean - True Basic - Statistics Graphics Toolkit 1.63142857142857 Midmean - MS Excel (old versions) 1.62954545454546 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503580099e83dum347eagk/1n4531225035764.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503580099e83dum347eagk/1n4531225035764.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503580099e83dum347eagk/24wdr1225035764.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t122503580099e83dum347eagk/24wdr1225035764.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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