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Central tendacy: Consumenten vertrouwen

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

Title produced by software: Central Tendency

Date of computation: Thu, 29 Nov 2007 11:51:46 -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/Nov/29/t1196361762849vb7u744vs88l.htm/, Retrieved Thu, 29 Nov 2007 19:42:42 +0100

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W11Q4G7

Dataseries X:

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0.095999941317353 -9.04408807056135 -5.09231333875753 7.34313713653525 6.63560018064468 3.32877271982314 2.66433993189590 -0.102551622536283 2.14800045472388 0.381767052098206 0.0520150966988598 -1.20429974984834 0.180933464398733 -0.623766913864838 -1.31699930330405 -3.40640402011230 -1.53027725362198 -4.86615759463456 -6.8264968223268 3.35606979091632 0.686295503992223 -1.77200501850743 -3.95774549279631 0.0345911855711826 4.63103090010043 -9.3080691781087 6.37194274609009 -0.0403904518462921 3.01666014093676 2.56424393277592 -0.988465785187376 0.23728358546037 -1.26100846567544 5.7468830292534 -2.52566837773900 2.49279610634753 1.46667487829410 -3.63179212590862 -0.535790141982679 0.603558137290495 0.174634385554984 3.06507606351888 1.65602728803071 -1.88476789218229 -5.80346444273218 -1.04548848092358 -1.69590743134157 -0.259433288445087 -4.90457543861949 3.33394982982317 -1.49406280930126 3.21349913534698 4.32420431407568 0.802285271849902 -1.58934873264713 1.14274861482444 -1.84219466957676 3.83591036015116 1.00529871442092 1.09713644310019 0.680043721142344 5.25197993911332 1.07071514425464 -6.68901009949608 6.44178681543623 3.26718864984128 -0.304065598533939 4.20123373389104 1.84426294601811 1.29559239481646 -0.24915579874099 0.129019730509375 0.76346286911035

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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 0.230669696851161 0.405907341365771 0.568281657767062 Geometric Mean NaN Harmonic Mean 1.68267624745219 Quadratic Mean 3.45195364001585 Winsorized Mean ( 1 / 24 ) 0.22459358933961 0.402486904923162 0.55801464989895 Winsorized Mean ( 2 / 24 ) 0.280039558737585 0.383732378334522 0.729778289632518 Winsorized Mean ( 3 / 24 ) 0.282819393812294 0.381650842017125 0.741042237238412 Winsorized Mean ( 4 / 24 ) 0.297092596000086 0.362434135714507 0.819714719791486 Winsorized Mean ( 5 / 24 ) 0.311904103796975 0.344505204152171 0.905368337075116 Winsorized Mean ( 6 / 24 ) 0.276297708820960 0.331401160305865 0.83372583417014 Winsorized Mean ( 7 / 24 ) 0.250559884241799 0.325354758073875 0.770112863033362 Winsorized Mean ( 8 / 24 ) 0.336635667436715 0.302254040893344 1.11375075893693 Winsorized Mean ( 9 / 24 ) 0.331781830975486 0.286598816076708 1.15765248271886 Winsorized Mean ( 10 / 24 ) 0.296925329134593 0.269924599758545 1.10003063596353 Winsorized Mean ( 11 / 24 ) 0.426305774258999 0.245592578659236 1.73582514824483 Winsorized Mean ( 12 / 24 ) 0.530808246953248 0.228897889960898 2.31897396277407 Winsorized Mean ( 13 / 24 ) 0.52742275358486 0.225935525289105 2.33439496913987 Winsorized Mean ( 14 / 24 ) 0.530587163338976 0.222256297133098 2.38727617702204 Winsorized Mean ( 15 / 24 ) 0.515725762380981 0.214944644911607 2.39934222410177 Winsorized Mean ( 16 / 24 ) 0.528469384542586 0.209891299169842 2.51782416247256 Winsorized Mean ( 17 / 24 ) 0.460178584401941 0.194736452015436 2.3630839508438 Winsorized Mean ( 18 / 24 ) 0.444426968150069 0.189612166586655 2.34387368780453 Winsorized Mean ( 19 / 24 ) 0.471915980640583 0.180270696149327 2.61781859570606 Winsorized Mean ( 20 / 24 ) 0.3927913740666 0.163736916778345 2.39891761610689 Winsorized Mean ( 21 / 24 ) 0.321728296663147 0.148699551542677 2.16361309314917 Winsorized Mean ( 22 / 24 ) 0.312860672562077 0.133926597366217 2.33606078788496 Winsorized Mean ( 23 / 24 ) 0.271167748972908 0.123205254898593 2.20094304578242 Winsorized Mean ( 24 / 24 ) 0.334822451826025 0.099000334492052 3.38203354103724 Trimmed Mean ( 1 / 24 ) 0.264842533967721 0.38175833817077 0.693743940831098 Trimmed Mean ( 2 / 24 ) 0.307424750748187 0.356691336472195 0.861878939333732 Trimmed Mean ( 3 / 24 ) 0.322343549380827 0.339079472553379 0.950643065926332 Trimmed Mean ( 4 / 24 ) 0.337139771721868 0.318744531287756 1.05771154836695 Trimmed Mean ( 5 / 24 ) 0.348740739292067 0.301755902551389 1.15570478106116 Trimmed Mean ( 6 / 24 ) 0.357557376640072 0.287259336346457 1.24471977547435 Trimmed Mean ( 7 / 24 ) 0.374314313789212 0.273539063816537 1.36841264485816 Trimmed Mean ( 8 / 24 ) 0.396956101651270 0.258291710477442 1.53685188315766 Trimmed Mean ( 9 / 24 ) 0.406963810055048 0.245848742896869 1.65534224523477 Trimmed Mean ( 10 / 24 ) 0.418469647524247 0.234408842268075 1.78521272267398 Trimmed Mean ( 11 / 24 ) 0.435867167607472 0.224185440716176 1.94422602206042 Trimmed Mean ( 12 / 24 ) 0.437162124406059 0.217232787114786 2.01241318224703 Trimmed Mean ( 13 / 24 ) 0.425041261026725 0.212068140082388 2.00426740604032 Trimmed Mean ( 14 / 24 ) 0.412265450844256 0.205978688377035 2.00149566002490 Trimmed Mean ( 15 / 24 ) 0.397917469096558 0.198804700454123 2.0015496021352 Trimmed Mean ( 16 / 24 ) 0.383933720462797 0.191070860432556 2.00937871737024 Trimmed Mean ( 17 / 24 ) 0.367024900786796 0.181902152247621 2.01770510272562 Trimmed Mean ( 18 / 24 ) 0.356213741957057 0.173627742855305 2.0515946132751 Trimmed Mean ( 19 / 24 ) 0.345992209398185 0.163606117913814 2.11478772193867 Trimmed Mean ( 20 / 24 ) 0.331331228057363 0.152228657186916 2.17653649569104 Trimmed Mean ( 21 / 24 ) 0.324094791511114 0.141549898231172 2.28961515028305 Trimmed Mean ( 22 / 24 ) 0.324378460023268 0.131245098925175 2.47154722484687 Trimmed Mean ( 23 / 24 ) 0.325793945687690 0.121347174302023 2.68480867034297 Trimmed Mean ( 24 / 24 ) 0.332729097618437 0.110355151067586 3.01507536711776 Median 0.180933464398733 Midrange -0.982466020786725 Midmean - Weighted Average at Xnp 0.294879569989867 Midmean - Weighted Average at X(n+1)p 0.356213741957057 Midmean - Empirical Distribution Function 0.356213741957057 Midmean - Empirical Distribution Function - Averaging 0.356213741957057 Midmean - Empirical Distribution Function - Interpolation 0.356213741957057 Midmean - Closest Observation 0.306569242073399 Midmean - True Basic - Statistics Graphics Toolkit 0.356213741957057 Midmean - MS Excel (old versions) 0.356213741957057 Number of observations 73

Charts produced by software:

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Parameters:

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')

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Software written by Ed van Stee & Patrick Wessa

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