*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 28 Apr 2010 14:11:39 +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/Apr/28/t1272464040o29p1729si6fobw.htm/, Retrieved Wed, 28 Apr 2010 16:14:00 +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/2010/Apr/28/t1272464040o29p1729si6fobw.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

1,4272 1,4614 1,4914 1,4816 1,4562 1,4268 1,4088 1,4016 1,365 1,319 1,305 1,2785 1,3239 1,3449 1,2732 1,3322 1,4369 1,4975 1,577 1,5553 1,5557 1,575 1,5527 1,4748 1,4718 1,457 1,4684 1,4227 1,3896 1,3622 1,3716 1,3419 1,3511 1,3516 1,3242 1,3074 1,2999 1,3213 1,2881 1,2611 1,2727 1,2811 1,2684 1,265 1,277 1,2271 1,202 1,1938 1,2103 1,1856 1,1786 1,2015 1,2256 1,2292 1,2037 1,2165 1,2694 1,2938 1,3201 1,3014 1,3119 1,3408 1,2991 1,249 1,2218 1,2176 1,2266 1,2138 1,2007 1,1985 1,2262 1,2646

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.3320125 0.0127449193500408 104.513215299062 Geometric Mean 1.32780358367739 Harmonic Mean 1.32371728852161 Quadratic Mean 1.33633455428355 Winsorized Mean ( 1 / 24 ) 1.33208194444444 0.0127212982548744 104.712735898164 Winsorized Mean ( 2 / 24 ) 1.33177361111111 0.0125456677508833 106.154063502705 Winsorized Mean ( 3 / 24 ) 1.33195277777778 0.0125115999341278 106.457430287922 Winsorized Mean ( 4 / 24 ) 1.33193055555556 0.0124571655189134 106.920836327760 Winsorized Mean ( 5 / 24 ) 1.32815277777778 0.0115722318153024 114.770668180144 Winsorized Mean ( 6 / 24 ) 1.32768611111111 0.0114622803369364 115.830888102845 Winsorized Mean ( 7 / 24 ) 1.32689861111111 0.0112486247625882 117.96096315029 Winsorized Mean ( 8 / 24 ) 1.32687638888889 0.0109924786658209 120.707661049602 Winsorized Mean ( 9 / 24 ) 1.32693888888889 0.0108569189905314 122.220575657435 Winsorized Mean ( 10 / 24 ) 1.32684166666667 0.0107138860486975 123.843175168730 Winsorized Mean ( 11 / 24 ) 1.32594027777778 0.0104927178078045 126.367667754444 Winsorized Mean ( 12 / 24 ) 1.32590694444444 0.0102591154410972 129.241838836608 Winsorized Mean ( 13 / 24 ) 1.32644861111111 0.0101359846406932 130.865294111219 Winsorized Mean ( 14 / 24 ) 1.3228125 0.00946178437744396 139.805817510856 Winsorized Mean ( 15 / 24 ) 1.320875 0.00911196133647944 144.960558020798 Winsorized Mean ( 16 / 24 ) 1.32089722222222 0.00908117926222865 145.454371517170 Winsorized Mean ( 17 / 24 ) 1.320425 0.0088508352058967 149.186485713833 Winsorized Mean ( 18 / 24 ) 1.3219 0.00759182777615414 174.121442026395 Winsorized Mean ( 19 / 24 ) 1.32319305555556 0.00686594141481658 192.718372559971 Winsorized Mean ( 20 / 24 ) 1.32083194444444 0.00621379681344403 212.564392447903 Winsorized Mean ( 21 / 24 ) 1.31569861111111 0.0054052796500178 243.409905925363 Winsorized Mean ( 22 / 24 ) 1.31472083333333 0.00497810304509873 264.100767184352 Winsorized Mean ( 23 / 24 ) 1.31414583333333 0.00480967739308853 273.229517476942 Winsorized Mean ( 24 / 24 ) 1.3117125 0.00417838396473197 313.928186368612 Trimmed Mean ( 1 / 24 ) 1.33070428571429 0.0124335356700182 107.025412644538 Trimmed Mean ( 2 / 24 ) 1.32924558823529 0.0120887387706523 109.957342403848 Trimmed Mean ( 3 / 24 ) 1.32786666666667 0.0117872588028545 112.652711616470 Trimmed Mean ( 4 / 24 ) 1.326334375 0.0114373553028296 115.965128290791 Trimmed Mean ( 5 / 24 ) 1.32470967741935 0.011031532064088 120.083925761482 Trimmed Mean ( 6 / 24 ) 1.32388333333333 0.0108295899225581 122.246857249477 Trimmed Mean ( 7 / 24 ) 1.32309655172414 0.0106107785049471 124.693635920047 Trimmed Mean ( 8 / 24 ) 1.32239821428571 0.0103949880190430 127.214982053193 Trimmed Mean ( 9 / 24 ) 1.32165185185185 0.0101867501878775 129.742246298005 Trimmed Mean ( 10 / 24 ) 1.32083846153846 0.00995424114112534 132.691025143192 Trimmed Mean ( 11 / 24 ) 1.319974 0.00969073229052018 136.209933411456 Trimmed Mean ( 12 / 24 ) 1.31916041666667 0.00940533967265448 140.256541770847 Trimmed Mean ( 13 / 24 ) 1.31828043478261 0.00909032166730765 145.020218538983 Trimmed Mean ( 14 / 24 ) 1.31725227272727 0.00870573338374193 151.308593390565 Trimmed Mean ( 15 / 24 ) 1.31657142857143 0.0083745343523119 157.211299540251 Trimmed Mean ( 16 / 24 ) 1.316055 0.00802338405329489 164.027421753487 Trimmed Mean ( 17 / 24 ) 1.31548157894737 0.00755419382289354 174.139241034656 Trimmed Mean ( 18 / 24 ) 1.3149 0.00697399364077623 188.543332232469 Trimmed Mean ( 19 / 24 ) 1.31407647058824 0.0065474424648926 200.700728205603 Trimmed Mean ( 20 / 24 ) 1.312996875 0.00615613790936927 213.28256356988 Trimmed Mean ( 21 / 24 ) 1.31205666666667 0.00580903316254305 225.864895233664 Trimmed Mean ( 22 / 24 ) 1.31161071428571 0.00558635037955141 234.788479986291 Trimmed Mean ( 23 / 24 ) 1.31121923076923 0.00538818656301634 243.350748054871 Trimmed Mean ( 24 / 24 ) 1.3108375 0.00512873692851213 255.586807877135 Median 1.30965 Midrange 1.3778 Midmean - Weighted Average at Xnp 1.31258378378378 Midmean - Weighted Average at X(n+1)p 1.3149 Midmean - Empirical Distribution Function 1.31258378378378 Midmean - Empirical Distribution Function - Averaging 1.3149 Midmean - Empirical Distribution Function - Interpolation 1.3149 Midmean - Closest Observation 1.31258378378378 Midmean - True Basic - Statistics Graphics Toolkit 1.3149 Midmean - MS Excel (old versions) 1.31548157894737 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Apr/28/t1272464040o29p1729si6fobw/11iqu1272463895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/28/t1272464040o29p1729si6fobw/11iqu1272463895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/28/t1272464040o29p1729si6fobw/21iqu1272463895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/28/t1272464040o29p1729si6fobw/21iqu1272463895.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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