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RES CT 4

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 06:09:34 -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/t1198587006jvq8f44248wp5rn.htm/, Retrieved Tue, 25 Dec 2007 13:50:06 +0100

User-defined keywords:

Klaas Van Pelt

Dataseries X:

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0.0920999483895251 -0.661235159527426 -0.545390217690751 1.84083710495651 1.46560381902488 -0.385977545699043 -6.66380275713979 -0.0308537217038178 2.99099773948675 -6.07956277426519 -3.32380776514134 -2.13534220368013 4.17726687644521 -1.88483511225136 4.32032586117556 5.01955700566159 -1.18473828988472 -3.52102075156362 -0.459480935761315 1.05369157570743 9.13157352610061 4.26114136236761 -7.87121212228509 1.55581634456701 -10.8887360210219 8.25296805537383 -1.83997332562592 -7.62224825377655 -5.40632098557146 2.59560800098151 3.37669355477046 2.51051188643414 -0.133112183983659 1.76509973840143 2.61993678174254 -2.13496336723294 -0.130859285441090 -2.17717514581710 3.32349169188177 -0.203694385559729 8.3942547620912 0.893649606235385 0.247317025903314 8.78115243855602 -1.25432061423584 10.1471620457646 -6.43495549200685 1.27193139250693 -15.6818171148577 4.37988560711793 11.2422582915534 3.20258069940299 -3.80525826075886 6.2472017910632 5.12525404526529 2.63104754246909 14.2559923818951 3.42817218699915 -11.3365485144944 2.78868989805804 5.41380690674063 -0.795184087460314 -0.522675955354885 5.03638977601517 -3.83618380577121 -2.04668547488907 4.77755094831181 -5.00099216112739 -11.0483905235327 -8.1477486460902 3.53824446863189 -1.79936835143724 0.222980922096426 0.0730330977356317 2.74600888141947 4.43935066443206 3.64533772778529 -0.213317787182433 1.77941996505484 -1.43955660877853

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 2 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 0.455181852974646 0.58758773984442 0.774661930650847 Geometric Mean NaN Harmonic Mean -2.60943232621714 Quadratic Mean 5.24239251949907 Winsorized Mean ( 1 / 26 ) 0.471826034349916 0.560650300346905 0.841569217135836 Winsorized Mean ( 2 / 26 ) 0.451652577979238 0.55236837499921 0.817665526162472 Winsorized Mean ( 3 / 26 ) 0.419555052335994 0.542686211879246 0.773108000815303 Winsorized Mean ( 4 / 26 ) 0.539083366705349 0.506024279621788 1.06533102938908 Winsorized Mean ( 5 / 26 ) 0.532185794664117 0.497385439465382 1.06996657408416 Winsorized Mean ( 6 / 26 ) 0.540261581798455 0.491312220787038 1.09962984623709 Winsorized Mean ( 7 / 26 ) 0.448621014626991 0.441764572456049 1.01552057950873 Winsorized Mean ( 8 / 26 ) 0.388166252708028 0.423910708833797 0.915679280138726 Winsorized Mean ( 9 / 26 ) 0.395685736537989 0.411049230593526 0.962623712898446 Winsorized Mean ( 10 / 26 ) 0.468732926468441 0.393062300212596 1.19251560430730 Winsorized Mean ( 11 / 26 ) 0.522151133905883 0.382349601057605 1.36563797232056 Winsorized Mean ( 12 / 26 ) 0.660571478606843 0.346514414630105 1.90633188899800 Winsorized Mean ( 13 / 26 ) 0.61063933354089 0.337605897126507 1.80873420381064 Winsorized Mean ( 14 / 26 ) 0.649974512620085 0.327986920534976 1.98170863508801 Winsorized Mean ( 15 / 26 ) 0.675784495210068 0.320481776729284 2.10865186191511 Winsorized Mean ( 16 / 26 ) 0.893274119313326 0.284841144793579 3.13604314419068 Winsorized Mean ( 17 / 26 ) 0.884340291258922 0.280974074240537 3.14740886200715 Winsorized Mean ( 18 / 26 ) 0.764741471011058 0.263793915886874 2.89901102699811 Winsorized Mean ( 19 / 26 ) 0.760272821393794 0.257392513878682 2.95374877045622 Winsorized Mean ( 20 / 26 ) 0.773217341645037 0.248111587879904 3.11640962944183 Winsorized Mean ( 21 / 26 ) 0.771480419674184 0.244691828732368 3.15286547847084 Winsorized Mean ( 22 / 26 ) 0.768016275281681 0.241218448739039 3.18390355006618 Winsorized Mean ( 23 / 26 ) 0.836700240958411 0.222886427162670 3.75393087685757 Winsorized Mean ( 24 / 26 ) 0.828796151346346 0.207300827724349 3.99803590002259 Winsorized Mean ( 25 / 26 ) 0.787319427259599 0.196279100928899 4.01122393333562 Winsorized Mean ( 26 / 26 ) 0.900053212639996 0.178809265083652 5.0335938253475 Trimmed Mean ( 1 / 26 ) 0.485132986806849 0.536869731507028 0.903632591550748 Trimmed Mean ( 2 / 26 ) 0.499140305182569 0.508803415038815 0.981008166276736 Trimmed Mean ( 3 / 26 ) 0.524809346914099 0.480871160059251 1.09137205660126 Trimmed Mean ( 4 / 26 ) 0.563792418980065 0.45206183915154 1.24715773407954 Trimmed Mean ( 5 / 26 ) 0.570852148201412 0.431969920594168 1.3215090240918 Trimmed Mean ( 6 / 26 ) 0.579950113739599 0.410782218455246 1.41181893393661 Trimmed Mean ( 7 / 26 ) 0.587967998980234 0.387037396002799 1.51915035873170 Trimmed Mean ( 8 / 26 ) 0.612851389043313 0.372004722272126 1.64742905762095 Trimmed Mean ( 9 / 26 ) 0.649090927161907 0.358169841683253 1.81224338741487 Trimmed Mean ( 10 / 26 ) 0.686632436883969 0.344357624609197 1.99395160093583 Trimmed Mean ( 11 / 26 ) 0.71668754176887 0.331673437770009 2.16082284607259 Trimmed Mean ( 12 / 26 ) 0.741952010322504 0.318499801801254 2.32952110527682 Trimmed Mean ( 13 / 26 ) 0.75199898954666 0.310086045601237 2.42513005733161 Trimmed Mean ( 14 / 26 ) 0.768727942920124 0.301336387022265 2.55106245387924 Trimmed Mean ( 15 / 26 ) 0.782299763525843 0.292323263936059 2.67614610275068 Trimmed Mean ( 16 / 26 ) 0.794134793338706 0.282446812210722 2.81162597348146 Trimmed Mean ( 17 / 26 ) 0.783358779645813 0.277254441259827 2.82541472045057 Trimmed Mean ( 18 / 26 ) 0.772558617975962 0.271124812546649 2.84945745363323 Trimmed Mean ( 19 / 26 ) 0.773385829294999 0.266577895647621 2.90116263171837 Trimmed Mean ( 20 / 26 ) 0.774766145916179 0.261620318366422 2.96141427681871 Trimmed Mean ( 21 / 26 ) 0.77492917794472 0.256716954865163 3.01861315841699 Trimmed Mean ( 22 / 26 ) 0.775294125909856 0.250481372561546 3.09521669408514 Trimmed Mean ( 23 / 26 ) 0.776072505656185 0.242409433945795 3.20149464904787 Trimmed Mean ( 24 / 26 ) 0.769482534427682 0.23574905136779 3.26398995017469 Trimmed Mean ( 25 / 26 ) 0.76289213254783 0.230194276535620 3.31412294010611 Trimmed Mean ( 26 / 26 ) 0.760100441723629 0.224796919633826 3.38127605556946 Median 0.23514897399987 Midrange -0.7129123664813 Midmean - Weighted Average at Xnp 0.705950252725807 Midmean - Weighted Average at X(n+1)p 0.774766145916179 Midmean - Empirical Distribution Function 0.705950252725807 Midmean - Empirical Distribution Function - Averaging 0.774766145916179 Midmean - Empirical Distribution Function - Interpolation 0.774766145916179 Midmean - Closest Observation 0.705950252725807 Midmean - True Basic - Statistics Graphics Toolkit 0.774766145916179 Midmean - MS Excel (old versions) 0.773385829294999 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198587006jvq8f44248wp5rn/153fv1198588169.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198587006jvq8f44248wp5rn/153fv1198588169.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198587006jvq8f44248wp5rn/23rnu1198588169.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/25/t1198587006jvq8f44248wp5rn/23rnu1198588169.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')

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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We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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