*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: Tue, 20 Oct 2009 12:43:14 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064259von525ruqy6ayfs.htm/, Retrieved Tue, 20 Oct 2009 20:44:19 +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/2009/Oct/20/t1256064259von525ruqy6ayfs.htm/}, year = {2009}, } @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 = {2009}, 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:

shwws3vr3dl3

Dataseries X:

» Textbox « » Textfile « » CSV «

0.012574783 0.012403995 0.007636115 0.010217099 0.011980207 0.008518714 0.011806494 0.008677247 0.007828065 0.0110378 0.013451951 0.011793506 0.013574772 0.016127754 0.009504169 0.012949032 0.012472433 0.011446595 0.014233108 0.010241215 0.010345286 0.014350612 0.011023946 0.012240217 0.012557682 0.012650476 0.00928352 0.011689686 0.011847985 0.013803522 0.011028207 0.011252228 0.011578129 0.015289385 0.012399675 0.011950452 0.012800277 0.014163763 0.010457464 0.010302347 0.012306248 0.012188573 0.011690144 0.011018659 0.009946478 0.010434684 0.015719071 0.010410347 0.011816245 0.01507051 0.007930064 0.011473243 0.013866003 0.013912725 0.015512261 0.009345681 0.012719274 0.016487412 0.024714911 0.016535084 0.019949145

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 0.0123366668032787 0.000362845643641047 33.9997655187036 Geometric Mean 0.0120547860323539 Harmonic Mean 0.0117962912875032 Quadratic Mean 0.0126527769869573 Winsorized Mean ( 1 / 20 ) 0.0122616862131148 0.000324114062810468 37.8313921549434 Winsorized Mean ( 2 / 20 ) 0.0121530940163934 0.000286444722773219 42.427362245438 Winsorized Mean ( 3 / 20 ) 0.0121796994918033 0.000279118233076417 43.6363449193544 Winsorized Mean ( 4 / 20 ) 0.0121665109672131 0.000270957314290378 44.9019470062158 Winsorized Mean ( 5 / 20 ) 0.0121827068688525 0.000252864972370092 48.1787048426062 Winsorized Mean ( 6 / 20 ) 0.0121684790983607 0.000247032407062897 49.2586346991406 Winsorized Mean ( 7 / 20 ) 0.0121610903114754 0.000237918429176048 51.1145368334489 Winsorized Mean ( 8 / 20 ) 0.0121903931311475 0.000221342620550726 55.0747664449641 Winsorized Mean ( 9 / 20 ) 0.0121241063606557 0.00019284793028378 62.8687398553609 Winsorized Mean ( 10 / 20 ) 0.0121087968524590 0.000188533253530769 64.2263188360182 Winsorized Mean ( 11 / 20 ) 0.0121073158196721 0.000184387367949175 65.6623930062793 Winsorized Mean ( 12 / 20 ) 0.0120663783114754 0.000174040214298673 69.3309782460282 Winsorized Mean ( 13 / 20 ) 0.0120702866229508 0.000170012531526860 70.9964525235237 Winsorized Mean ( 14 / 20 ) 0.0120615322622951 0.000166591656774800 72.4017786713052 Winsorized Mean ( 15 / 20 ) 0.0120108839016393 0.000156066036389903 76.9602674577594 Winsorized Mean ( 16 / 20 ) 0.0121258672459016 0.000127583570700562 95.0425448928765 Winsorized Mean ( 17 / 20 ) 0.0119871829180328 0.000104317773710921 114.910264009765 Winsorized Mean ( 18 / 20 ) 0.0119445453442623 9.75351256427692e-05 122.464038114948 Winsorized Mean ( 19 / 20 ) 0.0119223028852459 9.34261506532991e-05 127.612052962442 Winsorized Mean ( 20 / 20 ) 0.0119700504262295 7.93443143524911e-05 150.862106805183 Trimmed Mean ( 1 / 20 ) 0.0122065364237288 0.000298813775957312 40.8499788358908 Trimmed Mean ( 2 / 20 ) 0.0121475164736842 0.000266222830755946 45.6291312025758 Trimmed Mean ( 3 / 20 ) 0.0121444234727273 0.000252391610148301 48.1173818162634 Trimmed Mean ( 4 / 20 ) 0.0121308899056604 0.000238810932467829 50.7970459321186 Trimmed Mean ( 5 / 20 ) 0.0121202385098039 0.000225151926945343 53.8313781020679 Trimmed Mean ( 6 / 20 ) 0.0121046851632653 0.000214541240910733 56.421250813506 Trimmed Mean ( 7 / 20 ) 0.0120908857659574 0.000202921649566044 59.5840108328229 Trimmed Mean ( 8 / 20 ) 0.0120772906 0.000190818649948947 63.2919822209792 Trimmed Mean ( 9 / 20 ) 0.0120572346279070 0.000180098192230845 66.9481157948123 Trimmed Mean ( 10 / 20 ) 0.0120461799512195 0.000174481057628807 69.0400443172846 Trimmed Mean ( 11 / 20 ) 0.0120363860256410 0.000168111032345864 71.5978354167616 Trimmed Mean ( 12 / 20 ) 0.0120257552702703 0.000160579069977262 74.8899297521972 Trimmed Mean ( 13 / 20 ) 0.0120198552571429 0.000153285089890346 78.415032184418 Trimmed Mean ( 14 / 20 ) 0.0120126843636364 0.000144206764818756 83.3018088904102 Trimmed Mean ( 15 / 20 ) 0.0120058186451613 0.000132232681238252 90.7931271810912 Trimmed Mean ( 16 / 20 ) 0.0120051083448276 0.000118500830785330 101.308220923576 Trimmed Mean ( 17 / 20 ) 0.0119880567407407 0.000108919717794963 110.063237248812 Trimmed Mean ( 18 / 20 ) 0.01198818216 0.000103884527998265 115.399110830058 Trimmed Mean ( 19 / 20 ) 0.0119946117391304 9.83379261821963e-05 121.9734054276 Trimmed Mean ( 20 / 20 ) 0.0120056664761905 9.0632768978723e-05 132.464963958112 Median 0.011950452 Midrange 0.016175513 Midmean - Weighted Average at Xnp 0.0119535202 Midmean - Weighted Average at X(n+1)p 0.0120058186451613 Midmean - Empirical Distribution Function 0.0120058186451613 Midmean - Empirical Distribution Function - Averaging 0.0120058186451613 Midmean - Empirical Distribution Function - Interpolation 0.0120058186451613 Midmean - Closest Observation 0.0119567206875 Midmean - True Basic - Statistics Graphics Toolkit 0.0120058186451613 Midmean - MS Excel (old versions) 0.0120058186451613 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064259von525ruqy6ayfs/1w1eq1256064188.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064259von525ruqy6ayfs/1w1eq1256064188.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064259von525ruqy6ayfs/258zx1256064188.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064259von525ruqy6ayfs/258zx1256064188.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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