Centrummaten Superbenzine Loodvrij 98

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

Title produced by software: Central Tendency

Date of computation: Fri, 15 Aug 2008 03:10:53 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Aug/15/t1218791502kaoz3d050oc7q01.htm/, Retrieved Fri, 15 Aug 2008 09:11:44 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0,91 0,9 0,89 0,89 0,89 0,89 0,89 0,89 0,88 0,88 0,88 0,86 0,85 0,85 0,86 0,9 0,92 0,91 0,93 0,96 0,96 0,97 0,98 1,01 0,99 1,03 1,08 1,06 1,1 1,17 1,16 1,12 1,17 1,13 1,12 1,07 1,04 1,08 1,06 1,12 1,18 1,13 1,08 1,06 1,09 1,02 1,01 1,01 1 1,01 1,03 1,09 1,07 1,05 1,06 1,06 1,08 1,07 1,04 1,04 1,06 1,09 1,09 1,05 1,01 1,02 1,03 1,06 1,08 1,05 1,05 1,05 1,04 1,05 1,07 1,1 1,16 1,16 1,17 1,17 1,18 1,21 1,18 1,13 1,12 1,17 1,19 1,26 1,25 1,28 1,35 1,39 1,45 1,41 1,32 1,31

Text written by user:

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.06447916666667 0.0131070740506083 81.2140957285022 Geometric Mean 1.05702466600068 Harmonic Mean 1.04975152675650 Quadratic Mean 1.07211774462199 Winsorized Mean ( 1 / 32 ) 1.0640625 0.0129841148941055 81.951100146461 Winsorized Mean ( 2 / 32 ) 1.06385416666667 0.0128344466864402 82.8905361218762 Winsorized Mean ( 3 / 32 ) 1.06260416666667 0.0125159939709321 84.89970266321 Winsorized Mean ( 4 / 32 ) 1.0621875 0.0120872224155794 87.8768887905077 Winsorized Mean ( 5 / 32 ) 1.06166666666667 0.0119718847050835 88.6799942381553 Winsorized Mean ( 6 / 32 ) 1.05979166666667 0.0115792266795791 91.5252543190726 Winsorized Mean ( 7 / 32 ) 1.0590625 0.0111774739451210 94.7497176195414 Winsorized Mean ( 8 / 32 ) 1.05822916666667 0.0110223007513105 96.008010536353 Winsorized Mean ( 9 / 32 ) 1.05447916666667 0.0103818222039000 101.569757789778 Winsorized Mean ( 10 / 32 ) 1.05239583333333 0.0100674749788033 104.534238778752 Winsorized Mean ( 11 / 32 ) 1.05125 0.00990663653155908 106.115733291626 Winsorized Mean ( 12 / 32 ) 1.05125 0.00990663653155908 106.115733291626 Winsorized Mean ( 13 / 32 ) 1.05260416666667 0.00967820484077799 108.760269490437 Winsorized Mean ( 14 / 32 ) 1.05114583333333 0.0094809016148933 110.869817663978 Winsorized Mean ( 15 / 32 ) 1.05270833333333 0.00922249248793722 114.145751239185 Winsorized Mean ( 16 / 32 ) 1.05270833333333 0.00922249248793722 114.145751239185 Winsorized Mean ( 17 / 32 ) 1.05447916666667 0.00893798050072199 117.977340248336 Winsorized Mean ( 18 / 32 ) 1.05635416666667 0.0086451991946685 122.189685035611 Winsorized Mean ( 19 / 32 ) 1.0603125 0.00749188614464915 141.528111816982 Winsorized Mean ( 20 / 32 ) 1.0603125 0.00749188614464915 141.528111816982 Winsorized Mean ( 21 / 32 ) 1.0625 0.00718947817934153 147.785412723418 Winsorized Mean ( 22 / 32 ) 1.05791666666667 0.00594181706706623 178.045984035825 Winsorized Mean ( 23 / 32 ) 1.0603125 0.00561844769448057 188.719831109512 Winsorized Mean ( 24 / 32 ) 1.0628125 0.0052975149855314 200.624727424605 Winsorized Mean ( 25 / 32 ) 1.0628125 0.00463516101699917 229.293544733872 Winsorized Mean ( 26 / 32 ) 1.0628125 0.00463516101699917 229.293544733872 Winsorized Mean ( 27 / 32 ) 1.0628125 0.00463516101699917 229.293544733872 Winsorized Mean ( 28 / 32 ) 1.0628125 0.00463516101699917 229.293544733872 Winsorized Mean ( 29 / 32 ) 1.05677083333333 0.00388568784035595 271.964933044268 Winsorized Mean ( 30 / 32 ) 1.05989583333333 0.00349967038443732 302.85590267203 Winsorized Mean ( 31 / 32 ) 1.05666666666667 0.00312273309591199 338.378796461971 Winsorized Mean ( 32 / 32 ) 1.06 0.00272255040389602 389.340817522834 Trimmed Mean ( 1 / 32 ) 1.06265957446809 0.0125269560932286 84.8298314897506 Trimmed Mean ( 2 / 32 ) 1.06119565217391 0.0120009977202132 88.425619012205 Trimmed Mean ( 3 / 32 ) 1.05977777777778 0.0114873624072543 92.2559714063276 Trimmed Mean ( 4 / 32 ) 1.05875 0.0110378522521661 95.919928606784 Trimmed Mean ( 5 / 32 ) 1.05779069767442 0.0106715689921808 99.1223219799706 Trimmed Mean ( 6 / 32 ) 1.05690476190476 0.0102828279985990 102.783471827863 Trimmed Mean ( 7 / 32 ) 1.05634146341463 0.0099388558203257 106.284011209252 Trimmed Mean ( 8 / 32 ) 1.055875 0.00963691109120276 109.565709386265 Trimmed Mean ( 9 / 32 ) 1.05551282051282 0.00932030291800814 113.248767749106 Trimmed Mean ( 10 / 32 ) 1.05565789473684 0.00908504753111723 116.197289130421 Trimmed Mean ( 11 / 32 ) 1.05608108108108 0.00886948762447719 119.069006665797 Trimmed Mean ( 12 / 32 ) 1.05666666666667 0.0086444279501474 122.236737093592 Trimmed Mean ( 13 / 32 ) 1.05728571428571 0.00837753435853435 126.204879507135 Trimmed Mean ( 14 / 32 ) 1.05779411764706 0.0081033859219012 130.53729982033 Trimmed Mean ( 15 / 32 ) 1.05848484848485 0.00780963013263142 135.535848754491 Trimmed Mean ( 16 / 32 ) 1.0590625 0.00750568154509297 141.101443438190 Trimmed Mean ( 17 / 32 ) 1.05967741935484 0.00713608649077211 148.495596392384 Trimmed Mean ( 18 / 32 ) 1.06016666666667 0.00674177325273826 157.253385262707 Trimmed Mean ( 19 / 32 ) 1.06051724137931 0.00631604805431262 167.908355392449 Trimmed Mean ( 20 / 32 ) 1.06053571428571 0.00602710136258545 175.961154539265 Trimmed Mean ( 21 / 32 ) 1.06055555555556 0.00566609114518953 187.175872815947 Trimmed Mean ( 22 / 32 ) 1.06038461538462 0.00527495532968111 201.022482487775 Trimmed Mean ( 23 / 32 ) 1.0606 0.00505003536055513 210.018331412914 Trimmed Mean ( 24 / 32 ) 1.060625 0.00483235117802933 219.484255370805 Trimmed Mean ( 25 / 32 ) 1.06043478260870 0.00462043896255316 229.509531714 Trimmed Mean ( 26 / 32 ) 1.06022727272727 0.00448733991232629 236.270773652544 Trimmed Mean ( 27 / 32 ) 1.06 0.00431080537409043 245.893727044835 Trimmed Mean ( 28 / 32 ) 1.05975 0.00407442775595071 260.097874714365 Trimmed Mean ( 29 / 32 ) 1.05947368421053 0.00375166854147591 282.400663197642 Trimmed Mean ( 30 / 32 ) 1.05972222222222 0.00352960520097922 300.23817449278 Trimmed Mean ( 31 / 32 ) 1.05970588235294 0.00333739398257773 317.524957462304 Trimmed Mean ( 32 / 32 ) 1.06 0.00317500317500477 333.857933858101 Median 1.06 Midrange 1.15 Midmean - Weighted Average at Xnp 1.06196078431373 Midmean - Weighted Average at X(n+1)p 1.0634 Midmean - Empirical Distribution Function 1.06196078431373 Midmean - Empirical Distribution Function - Averaging 1.0634 Midmean - Empirical Distribution Function - Interpolation 1.0634 Midmean - Closest Observation 1.06196078431373 Midmean - True Basic - Statistics Graphics Toolkit 1.0634 Midmean - MS Excel (old versions) 1.06196078431373 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218791502kaoz3d050oc7q01/1mt6l1218791448.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218791502kaoz3d050oc7q01/1mt6l1218791448.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218791502kaoz3d050oc7q01/2n64x1218791448.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218791502kaoz3d050oc7q01/2n64x1218791448.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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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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