*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 09:49:47 -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/t1225036213fck8ok6ajkqll7g.htm/, Retrieved Sun, 26 Oct 2008 15:50:15 +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/t1225036213fck8ok6ajkqll7g.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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8,7800 8,8300 8,8300 8,8500 8,7400 8,7100 8,6800 8,5900 8,6400 8,6100 8,5900 8,5800 8,5700 8,5600 8,5500 8,5700 8,5300 8,5900 8,5500 8,5400 8,5600 8,5300 8,5500 8,5600 8,4800 8,5000 8,5400 8,4900 8,5100 8,5000 8,5900 8,5600 8,4500 8,4800 8,4800 8,4900 8,5200 8,4900 8,5700 8,5900 8,5700 8,5300 8,5700 8,5300 8,5400 8,4800 8,4800 8,5300 8,5700 8,4900 8,5400 8,5400 8,5600 8,6100 8,6700 8,6900 8,6900 8,7200 8,6600 8,6000 8,1100 8,1400 8,1800 8,1900 8,2200 8,2800 8,2800 8,3400 8,4100 8,3800 8,3800 8,3800 8,3900 8,4200 8,4400 8,4400 8,4400 8,4300 8,4000 8,4200

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 8.519625 0.016174917828915 526.718286306837 Geometric Mean 8.51840503330904 Harmonic Mean 8.5171778322452 Quadratic Mean 8.5208379136092 Winsorized Mean ( 1 / 26 ) 8.51975 0.0159954255723474 532.63665674071 Winsorized Mean ( 2 / 26 ) 8.52075 0.015707749236474 542.455183853743 Winsorized Mean ( 3 / 26 ) 8.51925 0.015166559442288 561.712762371556 Winsorized Mean ( 4 / 26 ) 8.51875 0.0143491443312127 593.676515014887 Winsorized Mean ( 5 / 26 ) 8.52125 0.0131764738084708 646.701850879248 Winsorized Mean ( 6 / 26 ) 8.5205 0.0130358561016835 653.620286503443 Winsorized Mean ( 7 / 26 ) 8.524 0.0115692740163686 736.779160726933 Winsorized Mean ( 8 / 26 ) 8.528 0.0108184090643469 788.285962314442 Winsorized Mean ( 9 / 26 ) 8.526875 0.0106089789860562 803.741341292807 Winsorized Mean ( 10 / 26 ) 8.525625 0.0103847559742908 820.974996534014 Winsorized Mean ( 11 / 26 ) 8.525625 0.00990435869718638 860.795257993024 Winsorized Mean ( 12 / 26 ) 8.524125 0.00914664936576522 931.939627193402 Winsorized Mean ( 13 / 26 ) 8.520875 0.0081349257774772 1047.44348419150 Winsorized Mean ( 14 / 26 ) 8.522625 0.00783885112917169 1087.22883743559 Winsorized Mean ( 15 / 26 ) 8.52075 0.00758240593392594 1123.75281332217 Winsorized Mean ( 16 / 26 ) 8.52075 0.00699180125648082 1218.67737474688 Winsorized Mean ( 17 / 26 ) 8.522875 0.0066494354714222 1281.74414754898 Winsorized Mean ( 18 / 26 ) 8.522875 0.0066494354714222 1281.74414754898 Winsorized Mean ( 19 / 26 ) 8.522875 0.0066494354714222 1281.74414754898 Winsorized Mean ( 20 / 26 ) 8.525375 0.00626155577282538 1361.54261166201 Winsorized Mean ( 21 / 26 ) 8.530625 0.00478110650690608 1784.23655437877 Winsorized Mean ( 22 / 26 ) 8.527875 0.0044355217109266 1922.63177947978 Winsorized Mean ( 23 / 26 ) 8.527875 0.0044355217109266 1922.63177947978 Winsorized Mean ( 24 / 26 ) 8.527875 0.0044355217109266 1922.63177947978 Winsorized Mean ( 25 / 26 ) 8.527875 0.0044355217109266 1922.63177947978 Winsorized Mean ( 26 / 26 ) 8.531125 0.00400155725225043 2131.95125352816 Trimmed Mean ( 1 / 26 ) 8.52064102564102 0.0151387629165557 562.836017223237 Trimmed Mean ( 2 / 26 ) 8.52157894736842 0.0141161256942833 603.676896332785 Trimmed Mean ( 3 / 26 ) 8.52202702702703 0.0130784941646987 651.606134445475 Trimmed Mean ( 4 / 26 ) 8.52305555555555 0.0120893240595291 705.006790585404 Trimmed Mean ( 5 / 26 ) 8.52428571428571 0.0112206763977415 759.694461556834 Trimmed Mean ( 6 / 26 ) 8.525 0.0105812214600017 805.672580639721 Trimmed Mean ( 7 / 26 ) 8.52590909090909 0.0098448980378957 866.023097252053 Trimmed Mean ( 8 / 26 ) 8.52625 0.00937400788401224 909.562921804437 Trimmed Mean ( 9 / 26 ) 8.52596774193548 0.00899632593618334 947.716634814656 Trimmed Mean ( 10 / 26 ) 8.52583333333333 0.0085875078982247 992.81810676365 Trimmed Mean ( 11 / 26 ) 8.52586206896552 0.00813912036178845 1047.51640103429 Trimmed Mean ( 12 / 26 ) 8.52589285714286 0.00769878041325878 1107.43421678317 Trimmed Mean ( 13 / 26 ) 8.52611111111111 0.00732788375113903 1163.51615291193 Trimmed Mean ( 14 / 26 ) 8.52673076923077 0.00708556386056774 1203.39480908264 Trimmed Mean ( 15 / 26 ) 8.5272 0.0068454662487858 1245.67117711120 Trimmed Mean ( 16 / 26 ) 8.52791666666667 0.00659060106960124 1293.95127646266 Trimmed Mean ( 17 / 26 ) 8.52869565217391 0.00638997324204309 1334.69974428985 Trimmed Mean ( 18 / 26 ) 8.52931818181818 0.00620643571791285 1374.26996258111 Trimmed Mean ( 19 / 26 ) 8.53 0.00596154926897457 1430.8361157715 Trimmed Mean ( 20 / 26 ) 8.53075 0.00563172674708621 1514.76632001254 Trimmed Mean ( 21 / 26 ) 8.53131578947368 0.00529595047302582 1610.91306139035 Trimmed Mean ( 22 / 26 ) 8.53138888888889 0.00522741214584276 1632.04825846259 Trimmed Mean ( 23 / 26 ) 8.53176470588235 0.00519616251235238 1641.93569496730 Trimmed Mean ( 24 / 26 ) 8.5321875 0.00513397866134652 1661.90552450840 Trimmed Mean ( 25 / 26 ) 8.53266666666667 0.00502712946435052 1697.32383603314 Trimmed Mean ( 26 / 26 ) 8.53321428571429 0.00485377645556268 1758.05671394997 Median 8.54 Midrange 8.48 Midmean - Weighted Average at Xnp 8.53 Midmean - Weighted Average at X(n+1)p 8.53613636363636 Midmean - Empirical Distribution Function 8.53 Midmean - Empirical Distribution Function - Averaging 8.53613636363636 Midmean - Empirical Distribution Function - Interpolation 8.53613636363636 Midmean - Closest Observation 8.53 Midmean - True Basic - Statistics Graphics Toolkit 8.53613636363636 Midmean - MS Excel (old versions) 8.53 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036213fck8ok6ajkqll7g/1n3ap1225036185.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036213fck8ok6ajkqll7g/1n3ap1225036185.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036213fck8ok6ajkqll7g/2vd8j1225036185.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036213fck8ok6ajkqll7g/2vd8j1225036185.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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