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RES CT 2

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

Title produced by software: Central Tendency

Date of computation: Tue, 25 Dec 2007 06:05:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/25/t1198586790mmws3e15dfj6602.htm/, Retrieved Tue, 25 Dec 2007 13:46:30 +0100

User-defined keywords:

Klaas Van Pelt

Dataseries X:

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-0.506989902325989 4.88007967776828 1.21450068211499 27.8822644132403 4.36393480418803 4.34429314520993 4.85539101306677 2.66600851392888 8.28051837137848 6.23163376152634 -11.5390085155369 2.5510634563959 -3.04357152011076 8.33849793902137 11.7379487483667 3.45419323762339 -0.239377514124032 9.83139985460656 10.1425640912454 -9.96997686691292 -4.44916496608482 -4.43964945807339 11.9792892361410 -1.1892576028676 1.45333082023549 6.27326711354841 9.12179838003651 17.0318887661480 -6.03374596043278 9.71377174099858 -8.90439512965544 7.16319380546682 9.1117742507198 8.76751672914546 6.97897193233582 -0.624146779536742 1.34246749269283 -3.12035782536661 -1.81407113460095 3.84116987188008 -12.9504916860743 3.61395105319151 -11.7422028926221 5.1768015413771 4.84220949961766 -14.4563471903241 -1.80167294853758 13.0423515103157 -5.66647260942664 6.18049057913837 -4.90386336830106 -15.5576336716000 16.1110295774597 5.6008016787895 3.31811629022567 -3.68261900199427 -2.33060796595063 11.2985182313596 2.17465492335024 23.5820079889651 -9.27235736301466 -13.5159367678475 -9.00833983509705 0.630633628292465 -6.44449127383928 4.95739032793351 4.52795971406281 15.0746061480379

Text written by user:

Output produced by software:

Summary of compuational 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 2.3011397763366 1.06280815921612 2.16515064960907 Geometric Mean NaN Harmonic Mean -24.4687641149534 Quadratic Mean 8.99865787498859 Winsorized Mean ( 1 / 22 ) 2.25409610070426 1.0377519743694 2.17209521771711 Winsorized Mean ( 2 / 22 ) 2.08910466540013 0.979436827645645 2.13296519635869 Winsorized Mean ( 3 / 22 ) 2.07342463127152 0.964530903310315 2.14967153893714 Winsorized Mean ( 4 / 22 ) 2.08353435856742 0.935478852051487 2.22723833253769 Winsorized Mean ( 5 / 22 ) 1.94904463352059 0.902947548170844 2.15853582798789 Winsorized Mean ( 6 / 22 ) 1.99368899008964 0.856278184786034 2.32831926062419 Winsorized Mean ( 7 / 22 ) 2.04065888880828 0.837236396504832 2.43737479322127 Winsorized Mean ( 8 / 22 ) 2.02002206656246 0.822171250535017 2.45693590629441 Winsorized Mean ( 9 / 22 ) 1.88078552373815 0.79462785752975 2.36687589783842 Winsorized Mean ( 10 / 22 ) 2.1967766442054 0.71811424492934 3.05909075013761 Winsorized Mean ( 11 / 22 ) 2.24419266181987 0.703291995969173 3.19098279901117 Winsorized Mean ( 12 / 22 ) 2.20453971888647 0.67569666082856 3.2626174534934 Winsorized Mean ( 13 / 22 ) 2.34841628437934 0.65058910173925 3.60967664244791 Winsorized Mean ( 14 / 22 ) 2.37115411274679 0.624245465453413 3.79843225777304 Winsorized Mean ( 15 / 22 ) 2.27861662404547 0.609642517723889 3.73762747479084 Winsorized Mean ( 16 / 22 ) 2.44309918603046 0.578873709578686 4.22043555546613 Winsorized Mean ( 17 / 22 ) 2.30433333870946 0.516011671263537 4.46566127674386 Winsorized Mean ( 18 / 22 ) 2.27589451191898 0.506012968899673 4.49769996383279 Winsorized Mean ( 19 / 22 ) 2.27792268797901 0.448252942137558 5.08177966912255 Winsorized Mean ( 20 / 22 ) 2.41760018189889 0.423625147968818 5.70693263487947 Winsorized Mean ( 21 / 22 ) 2.40563481538688 0.420935909073983 5.71496696653664 Winsorized Mean ( 22 / 22 ) 2.41622278299077 0.36688142706084 6.58584110497938 Trimmed Mean ( 1 / 22 ) 2.18413445529164 0.986156801596176 2.21479429210085 Trimmed Mean ( 2 / 22 ) 2.10980020704074 0.92326080731119 2.28516166865689 Trimmed Mean ( 3 / 22 ) 2.12114937503721 0.886182616679297 2.39358043716269 Trimmed Mean ( 4 / 22 ) 2.13917872268203 0.848259804777442 2.52184379200107 Trimmed Mean ( 5 / 22 ) 2.15548827768114 0.813370341507792 2.65006992225138 Trimmed Mean ( 6 / 22 ) 2.20562459126298 0.781471921432117 2.82239774811228 Trimmed Mean ( 7 / 22 ) 2.25010490262035 0.756309202387992 2.97511242163365 Trimmed Mean ( 8 / 22 ) 2.28923217992590 0.730247278347451 3.13487259426209 Trimmed Mean ( 9 / 22 ) 2.33499789919769 0.701398402172136 3.32906076199563 Trimmed Mean ( 10 / 22 ) 2.40649429163113 0.671670241933797 3.58285084166097 Trimmed Mean ( 11 / 22 ) 2.43749603081581 0.653589317899413 3.72940004382222 Trimmed Mean ( 12 / 22 ) 2.46465435538548 0.633591869960439 3.88997156093461 Trimmed Mean ( 13 / 22 ) 2.49974918729408 0.613929206169758 4.07172221515533 Trimmed Mean ( 14 / 22 ) 2.51953887459832 0.594035201021668 4.24139658771908 Trimmed Mean ( 15 / 22 ) 2.53850534791769 0.573772218251148 4.42423886547701 Trimmed Mean ( 16 / 22 ) 2.57123207610900 0.54953266813244 4.67894308239619 Trimmed Mean ( 17 / 22 ) 2.58724868736882 0.524605978804844 4.93179413102208 Trimmed Mean ( 18 / 22 ) 2.62261310595124 0.50723710162638 5.17038895132518 Trimmed Mean ( 19 / 22 ) 2.66627396594049 0.484341551954828 5.5049457457847 Trimmed Mean ( 20 / 22 ) 2.71591285109346 0.468649757180757 5.79518672415728 Trimmed Mean ( 21 / 22 ) 2.75492296937275 0.45255110513856 6.0875400326981 Trimmed Mean ( 22 / 22 ) 2.80204914887878 0.42684222627412 6.56460157032189 Median 3.38615476392453 Midrange 6.16231537082015 Midmean - Weighted Average at Xnp 2.40810961052988 Midmean - Weighted Average at X(n+1)p 2.58724868736882 Midmean - Empirical Distribution Function 2.40810961052988 Midmean - Empirical Distribution Function - Averaging 2.58724868736882 Midmean - Empirical Distribution Function - Interpolation 2.58724868736882 Midmean - Closest Observation 2.40810961052988 Midmean - True Basic - Statistics Graphics Toolkit 2.58724868736882 Midmean - MS Excel (old versions) 2.57123207610900 Number of observations 68

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198586790mmws3e15dfj6602/18pfd1198587945.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198586790mmws3e15dfj6602/18pfd1198587945.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198586790mmws3e15dfj6602/2t5nm1198587945.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198586790mmws3e15dfj6602/2t5nm1198587945.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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')

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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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