jan-pieter onzea-centrummaten-aardappelprijs

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

Title produced by software: Central Tendency

Date of computation: Mon, 11 Aug 2008 06:45:12 -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/11/t1218458797zfzzo8pv1kyx0p6.htm/, Retrieved Mon, 11 Aug 2008 12:46:39 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0,31 0,32 0,31 0,32 0,31 0,91 0,68 0,48 0,43 0,39 0,44 0,5 0,56 0,59 0,6 0,59 0,59 0,78 0,64 0,47 0,4 0,36 0,36 0,36 0,36 0,35 0,35 0,35 0,33 0,78 0,71 0,62 0,52 0,46 0,43 0,43 0,42 0,42 0,42 0,42 0,43 0,99 1,03 0,83 0,64 0,6 0,58 0,58 0,58 0,57 0,57 0,56 0,56 0,88 0,84 0,69 0,59 0,54 0,52 0,52 0,51 0,52 0,51 0,51 0,53 0,95 0,98 0,88 0,81 0,77 0,76 0,75 0,73 0,74 0,73 0,75 0,77 1,09 1,03 0,9 0,76 0,66 0,63 0,61 0,61 0,61 0,61 0,61 0,62 0,76 0,83 0,81 0,77 0,75 0,76 0,76

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.609895833333333 0.0193997054099461 31.4384069471821 Geometric Mean 0.580318204092470 Harmonic Mean 0.550914873263138 Quadratic Mean 0.638534291692049 Winsorized Mean ( 1 / 32 ) 0.609270833333333 0.0192463512101637 31.6564332989822 Winsorized Mean ( 2 / 32 ) 0.609270833333333 0.0192463512101637 31.6564332989822 Winsorized Mean ( 3 / 32 ) 0.608333333333333 0.0189190720319393 32.1545016746245 Winsorized Mean ( 4 / 32 ) 0.607916666666667 0.0188314992896762 32.2819047658058 Winsorized Mean ( 5 / 32 ) 0.606875 0.0184327324344493 32.9237676594165 Winsorized Mean ( 6 / 32 ) 0.605625 0.0177684994405386 34.0841950118913 Winsorized Mean ( 7 / 32 ) 0.604895833333333 0.0176385460521778 34.2939736384139 Winsorized Mean ( 8 / 32 ) 0.603229166666667 0.0173518129340410 34.764619060827 Winsorized Mean ( 9 / 32 ) 0.604166666666667 0.0172097908350100 35.1059854508868 Winsorized Mean ( 10 / 32 ) 0.6 0.0165394265795084 36.2769529593834 Winsorized Mean ( 11 / 32 ) 0.598854166666667 0.016366733075713 36.5897191514244 Winsorized Mean ( 12 / 32 ) 0.598854166666667 0.016366733075713 36.5897191514244 Winsorized Mean ( 13 / 32 ) 0.600208333333333 0.0153654168299049 39.0622877320958 Winsorized Mean ( 14 / 32 ) 0.601666666666667 0.0151582779962918 39.6922834383861 Winsorized Mean ( 15 / 32 ) 0.600104166666667 0.0140733470186903 42.6411830724908 Winsorized Mean ( 16 / 32 ) 0.600104166666667 0.0140733470186903 42.6411830724908 Winsorized Mean ( 17 / 32 ) 0.598333333333333 0.0138385637966234 43.2366640156203 Winsorized Mean ( 18 / 32 ) 0.598333333333333 0.0138385637966234 43.2366640156203 Winsorized Mean ( 19 / 32 ) 0.6003125 0.0135735917535524 44.2265032645387 Winsorized Mean ( 20 / 32 ) 0.598229166666667 0.0133031413580661 44.969015254727 Winsorized Mean ( 21 / 32 ) 0.598229166666667 0.0133031413580661 44.969015254727 Winsorized Mean ( 22 / 32 ) 0.598229166666667 0.0133031413580661 44.969015254727 Winsorized Mean ( 23 / 32 ) 0.600625 0.0129876902751879 46.2457132310472 Winsorized Mean ( 24 / 32 ) 0.605625 0.0123515860370877 49.0321646290210 Winsorized Mean ( 25 / 32 ) 0.605625 0.0116902760799119 51.8058765986442 Winsorized Mean ( 26 / 32 ) 0.608333333333333 0.0113638649631446 53.5322564379538 Winsorized Mean ( 27 / 32 ) 0.613958333333333 0.0107140659786713 57.3039530049145 Winsorized Mean ( 28 / 32 ) 0.613958333333333 0.0100027180151226 61.3791503874367 Winsorized Mean ( 29 / 32 ) 0.6109375 0.00960523217821248 63.6046571977498 Winsorized Mean ( 30 / 32 ) 0.6109375 0.00960523217821248 63.6046571977498 Winsorized Mean ( 31 / 32 ) 0.607708333333333 0.00841427250124134 72.2235146584187 Winsorized Mean ( 32 / 32 ) 0.601041666666667 0.0075748880581542 79.346607111858 Trimmed Mean ( 1 / 32 ) 0.607978723404255 0.0188660341063435 32.2261011496756 Trimmed Mean ( 2 / 32 ) 0.606630434782609 0.0184325303267190 32.9108605291843 Trimmed Mean ( 3 / 32 ) 0.605222222222222 0.0179367927394287 33.7419421082912 Trimmed Mean ( 4 / 32 ) 0.604090909090909 0.0175107344026955 34.4983194421542 Trimmed Mean ( 5 / 32 ) 0.603023255813953 0.0170515190761054 35.3647820538746 Trimmed Mean ( 6 / 32 ) 0.602142857142857 0.0166397413850456 36.187032190537 Trimmed Mean ( 7 / 32 ) 0.601463414634146 0.0163337314915793 36.8233930467282 Trimmed Mean ( 8 / 32 ) 0.600875 0.0160084963102074 37.5347558169388 Trimmed Mean ( 9 / 32 ) 0.60051282051282 0.0156913043062843 38.2704209153804 Trimmed Mean ( 10 / 32 ) 0.6 0.0153485812819433 39.0915609057538 Trimmed Mean ( 11 / 32 ) 0.6 0.0150747858019673 39.8015605582733 Trimmed Mean ( 12 / 32 ) 0.600138888888889 0.0147825832462311 40.5977006110823 Trimmed Mean ( 13 / 32 ) 0.600285714285714 0.0144362257539677 41.5819012888967 Trimmed Mean ( 14 / 32 ) 0.600294117647059 0.0141978534470442 42.2806250174411 Trimmed Mean ( 15 / 32 ) 0.600151515151515 0.0139454355003117 43.0356954530464 Trimmed Mean ( 16 / 32 ) 0.60015625 0.0138147684295073 43.4430915771349 Trimmed Mean ( 17 / 32 ) 0.60016129032258 0.0136502585201544 43.9670273963275 Trimmed Mean ( 18 / 32 ) 0.600333333333333 0.0134814513013328 44.5303194674586 Trimmed Mean ( 19 / 32 ) 0.60051724137931 0.0132691036450181 45.2568053912802 Trimmed Mean ( 20 / 32 ) 0.600535714285714 0.0130469174417172 46.0289349548207 Trimmed Mean ( 21 / 32 ) 0.600740740740741 0.0128117364406846 46.8898766004149 Trimmed Mean ( 22 / 32 ) 0.600961538461538 0.0125132196020969 48.0261321683215 Trimmed Mean ( 23 / 32 ) 0.6012 0.0121340808620739 49.5463980200679 Trimmed Mean ( 24 / 32 ) 0.60125 0.0117132744299935 51.3306508434919 Trimmed Mean ( 25 / 32 ) 0.600869565217391 0.0113010028495894 53.1695791262652 Trimmed Mean ( 26 / 32 ) 0.600454545454545 0.0109049058216145 55.06279057123 Trimmed Mean ( 27 / 32 ) 0.599761904761905 0.0104514145841826 57.3857155824246 Trimmed Mean ( 28 / 32 ) 0.5985 0.00998428251983573 59.9442172044874 Trimmed Mean ( 29 / 32 ) 0.597105263157895 0.00952579708277159 62.6829710909781 Trimmed Mean ( 30 / 32 ) 0.595833333333333 0.00900947473056198 66.1340811925633 Trimmed Mean ( 31 / 32 ) 0.594411764705882 0.00827546226281085 71.8282249170676 Trimmed Mean ( 32 / 32 ) 0.593125 0.00763900089523619 77.6443160740932 Median 0.59 Midrange 0.7 Midmean - Weighted Average at Xnp 0.610188679245283 Midmean - Weighted Average at X(n+1)p 0.613461538461539 Midmean - Empirical Distribution Function 0.610188679245283 Midmean - Empirical Distribution Function - Averaging 0.613461538461539 Midmean - Empirical Distribution Function - Interpolation 0.613461538461539 Midmean - Closest Observation 0.610188679245283 Midmean - True Basic - Statistics Graphics Toolkit 0.613461538461539 Midmean - MS Excel (old versions) 0.610188679245283 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218458797zfzzo8pv1kyx0p6/1ykm51218458709.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218458797zfzzo8pv1kyx0p6/1ykm51218458709.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218458797zfzzo8pv1kyx0p6/24ccb1218458709.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218458797zfzzo8pv1kyx0p6/24ccb1218458709.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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