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

Title produced by software: Central Tendency

Date of computation: Wed, 19 Dec 2007 09:25:27 -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/19/t1198080472slv3dav7p4odqod.htm/, Retrieved Wed, 19 Dec 2007 17:07:52 +0100

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Dataseries X:

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0.000397424338574195 -0.0202655604999885 0.0132814465175762 0.005102656127566 0.00395376151804691 -0.0201173449686611 -0.0247671428130995 0.0296498486252178 -0.0327107698022459 -0.0201214770451503 -0.00567361342843801 -0.00790813495132369 -0.00744834199983557 0.0334221780538597 0.0223155617292289 -0.00513034757815278 -0.0391719777595819 0.0107196708201284 0.00213285573769740 0.0287487067542047 0.0466321279413979 -0.0633887953481162 0.0116657789984877 0.0139234067539528 0.0359986505189924 0.0280558288935530 -0.0852872115347057 -0.0516809754337528 0.0302769602788920 -0.00118719973053998 0.0290023592650813 0.00862383582605371 -0.00222184141282044 0.0137756145454984 -0.0157531085361904 0.00326417246610666 -0.0129189887643890 0.0433055133466075 0.0423417932652459 0.0247880881888765 -0.0333941587119335 0.0278093375781444 0.0511443990799118 -0.00348464569037083 0.0383127002440179 -0.0340320422739696 -0.00961485948233042 -0.0456050161011798 0.0299553194649838 0.0476347599970703 0.0373863553011968 -0.0247794053542337 0.0578193759956714 0.0116813013386476 -0.0107218293589344 0.0137367155752570 0.000364587740733586 -0.0534378148244013 -0.0336231018728952 0.014152354464068 0.0039832977774554 0.0134276332689917 0.0109327863730047 -0.00806395326455454 -0.00412615912099392 -0.00406364317326485 -0.00400299337770367 -0.0421286178226839 -0.035341051310344 0.0152728466602875 -0.00507224805130227 -0.0544340564399082 0.0290775408303425 0.0136483853598492 0.0230238255628117 -0.00914535931783768 0.00680627292785807 0.0142485752260996 -0.0167461428598383

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 0.00119274280077946 0.00324189262594766 0.367915578459604 Geometric Mean NaN Harmonic Mean 0.0182456233002676 Quadratic Mean 0.0286564534380367 Winsorized Mean ( 1 / 26 ) 0.00138544456370135 0.00313960205447588 0.441280308670404 Winsorized Mean ( 2 / 26 ) 0.00152329519219165 0.00306545164797552 0.496923575094605 Winsorized Mean ( 3 / 26 ) 0.00152305251724865 0.00304937167648501 0.499464374577081 Winsorized Mean ( 4 / 26 ) 0.00144357022843134 0.00299793174404323 0.481522046424057 Winsorized Mean ( 5 / 26 ) 0.00176712967471054 0.00290304378318395 0.60871616368542 Winsorized Mean ( 6 / 26 ) 0.00172515285880684 0.00279573655955301 0.61706560044508 Winsorized Mean ( 7 / 26 ) 0.00190505242642667 0.00273039260183717 0.697721062218245 Winsorized Mean ( 8 / 26 ) 0.00215246727878449 0.00263426683123719 0.817102980328527 Winsorized Mean ( 9 / 26 ) 0.00200807271095126 0.002559920316955 0.784427818964242 Winsorized Mean ( 10 / 26 ) 0.00166170848640781 0.00248987038493363 0.667387546140119 Winsorized Mean ( 11 / 26 ) 0.00164880121827602 0.00247750460598484 0.665508840747683 Winsorized Mean ( 12 / 26 ) 0.00170620649471981 0.00245196381958505 0.695853046888984 Winsorized Mean ( 13 / 26 ) 0.00291719050093221 0.00221527992576678 1.31684960758287 Winsorized Mean ( 14 / 26 ) 0.00290604029412489 0.00221291583093942 1.31321772545286 Winsorized Mean ( 15 / 26 ) 0.00371260924391623 0.00207350529780501 1.79049903940268 Winsorized Mean ( 16 / 26 ) 0.00360146100982742 0.00204756928877076 1.75889579394381 Winsorized Mean ( 17 / 26 ) 0.00354930775588274 0.00203933137359683 1.74042718208308 Winsorized Mean ( 18 / 26 ) 0.00362904381856614 0.00182327084758479 1.99040302946399 Winsorized Mean ( 19 / 26 ) 0.00344355853064308 0.00172671078871945 1.99428795669765 Winsorized Mean ( 20 / 26 ) 0.00398174990740729 0.00160072595549252 2.48746507404645 Winsorized Mean ( 21 / 26 ) 0.00269369080698674 0.00126228462200949 2.13398053023773 Winsorized Mean ( 22 / 26 ) 0.00271672075297603 0.00118466582595621 2.29323805367916 Winsorized Mean ( 23 / 26 ) 0.00282539703470522 0.00116302843133377 2.42934476800799 Winsorized Mean ( 24 / 26 ) 0.00308437172123726 0.00111152780886551 2.77489388626754 Winsorized Mean ( 25 / 26 ) 0.00308691162781208 0.00109935768698526 2.80792290294276 Winsorized Mean ( 26 / 26 ) 0.00322543369758948 0.00107845679409469 2.99078620047738 Trimmed Mean ( 1 / 26 ) 0.00158044827013781 0.00303952300540909 0.519965885214643 Trimmed Mean ( 2 / 26 ) 0.00178585217425088 0.00292193077114645 0.611189078086946 Trimmed Mean ( 3 / 26 ) 0.00192792067824183 0.00283084254532854 0.681041296847571 Trimmed Mean ( 4 / 26 ) 0.00207808304781207 0.00273049752629567 0.761063882241016 Trimmed Mean ( 5 / 26 ) 0.00225970084756235 0.00263033657026395 0.859091902195464 Trimmed Mean ( 6 / 26 ) 0.00237585942265278 0.00254155391178553 0.934805833405933 Trimmed Mean ( 7 / 26 ) 0.00250766921379080 0.00246566120098651 1.01703722019371 Trimmed Mean ( 8 / 26 ) 0.00261562097388551 0.00239132501382745 1.09379568179194 Trimmed Mean ( 9 / 26 ) 0.00269059872370720 0.00232477331951194 1.15735960195554 Trimmed Mean ( 10 / 26 ) 0.00279214214180083 0.00226057739284297 1.23514556530593 Trimmed Mean ( 11 / 26 ) 0.00294881628000442 0.00219679182938340 1.34232849947922 Trimmed Mean ( 12 / 26 ) 0.00311857031285821 0.00212032863767217 1.47079573300580 Trimmed Mean ( 13 / 26 ) 0.00329400544121188 0.00203053837232840 1.62223254980140 Trimmed Mean ( 14 / 26 ) 0.00333890495898277 0.00197138503471044 1.69368484603171 Trimmed Mean ( 15 / 26 ) 0.00338875380522733 0.00189673129665025 1.7866282963813 Trimmed Mean ( 16 / 26 ) 0.00335246362131751 0.00183233560760005 1.82961222137057 Trimmed Mean ( 17 / 26 ) 0.00332514307452267 0.00175486327637987 1.89481603454723 Trimmed Mean ( 18 / 26 ) 0.00330091734288458 0.00165529588595884 1.99415546844817 Trimmed Mean ( 19 / 26 ) 0.00326579269304875 0.00157820799037173 2.06930437114282 Trimmed Mean ( 20 / 26 ) 0.00324684059970199 0.00149959551021525 2.16514425228969 Trimmed Mean ( 21 / 26 ) 0.00324684059970199 0.00142571934467782 2.27733502517335 Trimmed Mean ( 22 / 26 ) 0.0032194055177767 0.00141063690551010 2.28223542514829 Trimmed Mean ( 23 / 26 ) 0.0032741053751035 0.00140397067102698 2.33203260058741 Trimmed Mean ( 24 / 26 ) 0.00332382200748984 0.00139463684666076 2.38328853525433 Trimmed Mean ( 25 / 26 ) 0.00335100099113058 0.00138908795166488 2.41237495949357 Trimmed Mean ( 26 / 26 ) 0.00338190922772637 0.00137713343966613 2.45576000866428 Median 0.00326417246610666 Midrange -0.0137339177695171 Midmean - Weighted Average at Xnp 0.00277184187130468 Midmean - Weighted Average at X(n+1)p 0.00326579269304875 Midmean - Empirical Distribution Function 0.00326579269304875 Midmean - Empirical Distribution Function - Averaging 0.00326579269304875 Midmean - Empirical Distribution Function - Interpolation 0.00324684059970199 Midmean - Closest Observation 0.00277184187130468 Midmean - True Basic - Statistics Graphics Toolkit 0.00326579269304875 Midmean - MS Excel (old versions) 0.00326579269304875 Number of observations 79

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198080472slv3dav7p4odqod/1kk781198081521.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198080472slv3dav7p4odqod/1kk781198081521.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198080472slv3dav7p4odqod/2s6uz1198081521.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198080472slv3dav7p4odqod/2s6uz1198081521.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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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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