Central Tendency 2

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

Title produced by software: Central Tendency

Date of computation: Thu, 03 Jan 2008 12:37:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/03/t1199389105hlk2b6dgzhfx3q3.htm/, Retrieved Thu, 03 Jan 2008 20:38:26 +0100

User-defined keywords:

zonder outliers

Dataseries X:

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0.000416746290894009 -0.00506571540182827 -0.00218827952157368 -0.00346734519708139 -0.000266289106626969 0.00134211381399617 -0.00265793926885609 -0.00137561721744261 -0.00364269181053113 0.00138381567731760 0.00477337730066559 -0.00501968947558935 -0.00610125247805617 -0.00378421015341277 0.00468706870163177 0.00898260865928574 -0.00141007495854079 -0.00302448142362416 -0.0011265500194515 -0.00208354259785509 0.00432722909108169 -0.00512445206493861 -0.00180323806413446 -0.00201520685644990 -0.00366435098798135 -0.000551054372045334 -0.00536853904709989 -0.00157108888982482 -0.00392464902044615 0.00190602695788583 -0.00213891972227792 -0.00338442976396153 7.8443584912935e-05 -0.00528206357126715 0.00428208314608286 0.00413154271940847 -0.00500358535817375 -0.00178671762993171 -0.00720310728897305 0.000407109161799757 0.00374196413175365 -0.00575272002057342 -0.00171168321902748 -0.00400971064668304 0.000161569802361095 0.00384350249206233 0.00223795657888887 -0.00271268115930018 -0.00544114871331053 0.00128581727160632 -0.000261413305601532 -0.00647603834990773 -0.00195818972707368 0.00171581761496309 -0.00335087722529598 0.00118046884843115 0.00732365502444743 0.00226747516882936 -0.00108000962092014 -0.00270157723408593 0.00654605276007136 -0.00398937916670900 -0.00284746587393203 -0.00335713974223673 8.89253757249686e-05 -0.00232041032111008 -0.000519095298935734

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 -0.0010658694137101 0.000431785403464385 -2.46851654817002 Geometric Mean NaN Harmonic Mean 0.00421127388322971 Quadratic Mean 0.00366620068922123 Winsorized Mean ( 1 / 22 ) -0.00107977814051268 0.000421449741290316 -2.56205671690963 Winsorized Mean ( 2 / 22 ) -0.00109180251043879 0.000412570407960445 -2.64634227121656 Winsorized Mean ( 3 / 22 ) -0.00115557010753982 0.000389393110039645 -2.96761826993336 Winsorized Mean ( 4 / 22 ) -0.00114212158764555 0.000384969786977921 -2.96678239768216 Winsorized Mean ( 5 / 22 ) -0.00116355665811864 0.000378018182817269 -3.07804415503762 Winsorized Mean ( 6 / 22 ) -0.00115985550610366 0.000375833715050932 -3.08608690400881 Winsorized Mean ( 7 / 22 ) -0.00115911673658756 0.000369696533859328 -3.13531945914485 Winsorized Mean ( 8 / 22 ) -0.00118649626664556 0.000361197741025857 -3.28489392894798 Winsorized Mean ( 9 / 22 ) -0.00119395316077434 0.00035732687804123 -3.34134719257411 Winsorized Mean ( 10 / 22 ) -0.00141162254070101 0.000314143463988449 -4.49356011670169 Winsorized Mean ( 11 / 22 ) -0.00125329541626739 0.000287166062194871 -4.36435770539243 Winsorized Mean ( 12 / 22 ) -0.00130910403854124 0.000275904968820175 -4.74476427205799 Winsorized Mean ( 13 / 22 ) -0.00133345074834092 0.000267614353435970 -4.98273254487437 Winsorized Mean ( 14 / 22 ) -0.00137347885264793 0.000251575206108119 -5.45951595904745 Winsorized Mean ( 15 / 22 ) -0.00135598094919047 0.000246170048376549 -5.50831004069315 Winsorized Mean ( 16 / 22 ) -0.00136425255872829 0.00024320943457916 -5.60937350596179 Winsorized Mean ( 17 / 22 ) -0.00134649182388250 0.000232569411133444 -5.78963423143342 Winsorized Mean ( 18 / 22 ) -0.00152939523044237 0.000197080567444814 -7.76025384070719 Winsorized Mean ( 19 / 22 ) -0.00152438918626356 0.000195570362798105 -7.7945817784121 Winsorized Mean ( 20 / 22 ) -0.00159581510939726 0.000184525090807235 -8.64822828383992 Winsorized Mean ( 21 / 22 ) -0.00151628109632637 0.000166826992336614 -9.08894343228886 Winsorized Mean ( 22 / 22 ) -0.00146159836952992 0.00015848815382784 -9.22213007236872 Trimmed Mean ( 1 / 22 ) -0.00112604233982907 0.000405952906547592 -2.77382504637162 Trimmed Mean ( 2 / 22 ) -0.00117524394862586 0.00038712852407583 -3.03579786953558 Trimmed Mean ( 3 / 22 ) -0.00122106834500728 0.000370118229106822 -3.29913051825087 Trimmed Mean ( 4 / 22 ) -0.00124586146314469 0.000360558673485443 -3.45536400803013 Trimmed Mean ( 5 / 22 ) -0.00127634642655891 0.000350445331932605 -3.64206998997597 Trimmed Mean ( 6 / 22 ) -0.00130382611559708 0.000340245529959136 -3.83201541473205 Trimmed Mean ( 7 / 22 ) -0.00133415954589916 0.000328137711374607 -4.06585253584603 Trimmed Mean ( 8 / 22 ) -0.00136701071739461 0.000314645939711971 -4.34459989741479 Trimmed Mean ( 9 / 22 ) -0.00139786395259917 0.000299928253452574 -4.66066112981317 Trimmed Mean ( 10 / 22 ) -0.00143016187943667 0.000282051984589899 -5.07056130633547 Trimmed Mean ( 11 / 22 ) -0.00143292218098176 0.000271129385250771 -5.28501246611993 Trimmed Mean ( 12 / 22 ) -0.00145836614131128 0.000263515122112795 -5.53427875265177 Trimmed Mean ( 13 / 22 ) -0.00147869248457468 0.000256223665077713 -5.77110035533286 Trimmed Mean ( 14 / 22 ) -0.00149788616569433 0.000248429566105509 -6.02941988417823 Trimmed Mean ( 15 / 22 ) -0.00151397745908064 0.000241870681510129 -6.25945008972587 Trimmed Mean ( 16 / 22 ) -0.00153414082319995 0.000233943731795132 -6.55773425271093 Trimmed Mean ( 17 / 22 ) -0.00155569861433556 0.000223426356398408 -6.96291448964724 Trimmed Mean ( 18 / 22 ) -0.00158229606207817 0.000211375130015657 -7.48572484360372 Trimmed Mean ( 19 / 22 ) -0.00158908601556399 0.000205547122798476 -7.73100588287959 Trimmed Mean ( 20 / 22 ) -0.00159753569892292 0.000196819274049094 -8.11676451222166 Trimmed Mean ( 21 / 22 ) -0.00159776625791936 0.000187195505188359 -8.53528110256524 Trimmed Mean ( 22 / 22 ) -0.00160906958261238 0.000178608537368304 -9.00891752612226 Median -0.00178671762993171 Midrange 0.000889750685156345 Midmean - Weighted Average at Xnp -0.00161708076716484 Midmean - Weighted Average at X(n+1)p -0.00153414082319995 Midmean - Empirical Distribution Function -0.00153414082319995 Midmean - Empirical Distribution Function - Averaging -0.00153414082319995 Midmean - Empirical Distribution Function - Interpolation -0.00155569861433556 Midmean - Closest Observation -0.00161708076716484 Midmean - True Basic - Statistics Graphics Toolkit -0.00153414082319995 Midmean - MS Excel (old versions) -0.00153414082319995 Number of observations 67

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199389105hlk2b6dgzhfx3q3/1lcf81199389056.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199389105hlk2b6dgzhfx3q3/1lcf81199389056.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199389105hlk2b6dgzhfx3q3/25jij1199389056.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199389105hlk2b6dgzhfx3q3/25jij1199389056.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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