Central Tendancy - Verhandelde kapitalen Euronext Brussels

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 17 Mar 2010 09:18:17 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/17/t1268839640vgslvbx2vu05qpc.htm/, Retrieved Wed, 17 Mar 2010 16:27:22 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Mar/17/t1268839640vgslvbx2vu05qpc.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

3592,21 5955,74 4652,25 4211,65 4787,85 3599,73 4174,27 5106,33 5325,75 6604,61 5711,90 6919,30 7048,76 8655,98 6658,53 7247,03 8779,57 6602,49 9832,48 9369,49 8582,76 8206,94 6515,83 8618,10 8505,39 9881,64 9375,29 15642,50 12232,73 6288,93 12473,94 11142,82 10236,32 10581,51 8763,71 10819,04 11636,25 14650,13 10671,38 17468,63 13873,19 13077,58 16866,81 14186,64 19919,87 17681,78 9984,28 17423,09 13514,45 12334,57 12274,56 11752,23 13054,00 12460,98 8626,68 13722,62 12066,22 6798,83 6593,82 6606,19 6315,28 7232,95 6747,44 7803,61 6700,31 5369,53 8081,19 10718,39 9447,21 6815,10 5497,80 6805,31

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 9409.47597222222 441.851434969771 21.2955650418244 Geometric Mean 8703.53701065494 Harmonic Mean 8035.31974130394 Quadratic Mean 10119.2766096867 Winsorized Mean ( 1 / 24 ) 9378.49583333333 432.410448968593 21.6888742066788 Winsorized Mean ( 2 / 24 ) 9388.53444444445 427.950382572434 21.9383714252326 Winsorized Mean ( 3 / 24 ) 9388.19444444445 427.180186699938 21.977129878074 Winsorized Mean ( 4 / 24 ) 9381.76777777778 415.105167413923 22.6009419160584 Winsorized Mean ( 5 / 24 ) 9306.16291666667 393.109216401068 23.6732249675167 Winsorized Mean ( 6 / 24 ) 9250.00541666667 370.980990521988 24.933906731047 Winsorized Mean ( 7 / 24 ) 9226.27638888889 358.656475894072 25.7245498380847 Winsorized Mean ( 8 / 24 ) 9196.31305555556 351.251574439782 26.1815568235472 Winsorized Mean ( 9 / 24 ) 9193.52555555556 345.309262393968 26.6240340378317 Winsorized Mean ( 10 / 24 ) 9194.34916666667 335.601817965958 27.3966011936184 Winsorized Mean ( 11 / 24 ) 9164.85847222222 318.399480492543 28.7841502066674 Winsorized Mean ( 12 / 24 ) 9216.46013888889 310.079894730723 29.7228562557807 Winsorized Mean ( 13 / 24 ) 9116.48472222222 291.808550538616 31.2413214259662 Winsorized Mean ( 14 / 24 ) 9152.96055555556 286.231929240435 31.9774267666241 Winsorized Mean ( 15 / 24 ) 9142.87305555556 279.876771450788 32.6674950842185 Winsorized Mean ( 16 / 24 ) 9131.46416666666 277.494825842777 32.9067907444169 Winsorized Mean ( 17 / 24 ) 9122.08819444444 275.85842002903 33.0680071084453 Winsorized Mean ( 18 / 24 ) 9080.85569444444 269.250792294554 33.7263843016298 Winsorized Mean ( 19 / 24 ) 9011.80916666667 254.705079790716 35.3813483974148 Winsorized Mean ( 20 / 24 ) 8991.19805555556 248.338194909769 36.2054578790122 Winsorized Mean ( 21 / 24 ) 8861.02722222222 225.460400691513 39.301922621642 Winsorized Mean ( 22 / 24 ) 8777.79694444444 209.531555882613 41.8924820534531 Winsorized Mean ( 23 / 24 ) 8747.71486111111 204.871578081572 42.6985282342489 Winsorized Mean ( 24 / 24 ) 8735.30819444444 202.318048680108 43.1761192411269 Trimmed Mean ( 1 / 24 ) 9342.43128571428 420.343421403428 22.2257107165425 Trimmed Mean ( 2 / 24 ) 9304.24529411765 405.943385911505 22.9200563847737 Trimmed Mean ( 3 / 24 ) 9258.2693939394 391.539324987299 23.6458225345302 Trimmed Mean ( 4 / 24 ) 9209.5475 374.465712972515 24.593833776915 Trimmed Mean ( 5 / 24 ) 9159.54806451613 358.410263127563 25.5560429117961 Trimmed Mean ( 6 / 24 ) 9124.3605 346.333964658736 26.3455549587543 Trimmed Mean ( 7 / 24 ) 9098.365 338.091530540452 26.9109521479462 Trimmed Mean ( 8 / 24 ) 9074.87107142857 331.143813089783 27.4046221391069 Trimmed Mean ( 9 / 24 ) 9054.63074074074 324.282594539767 27.9220374241528 Trimmed Mean ( 10 / 24 ) 9033.2623076923 317.002315516951 28.4958874605106 Trimmed Mean ( 11 / 24 ) 9010.0658 309.944910601617 29.0698943322253 Trimmed Mean ( 12 / 24 ) 8988.95770833333 304.710624776825 29.4999812196145 Trimmed Mean ( 13 / 24 ) 8959.28347826087 299.444847123334 29.9196448505616 Trimmed Mean ( 14 / 24 ) 8939.49590909091 296.429015568056 30.1572904122084 Trimmed Mean ( 15 / 24 ) 8913.35738095238 293.113609963187 30.4092238571652 Trimmed Mean ( 16 / 24 ) 8885.8155 289.596703963515 30.6834137902325 Trimmed Mean ( 17 / 24 ) 8856.72552631579 284.874794989980 31.0898881967684 Trimmed Mean ( 18 / 24 ) 8825.5063888889 278.313390856752 31.7106782455588 Trimmed Mean ( 19 / 24 ) 8795.46529411765 270.569543572688 32.5072259722194 Trimmed Mean ( 20 / 24 ) 8769.845625 263.370839064510 33.2984686389366 Trimmed Mean ( 21 / 24 ) 8743.28333333333 254.361646051278 34.3734343171011 Trimmed Mean ( 22 / 24 ) 8728.86571428571 248.119594157485 35.1800741248406 Trimmed Mean ( 23 / 24 ) 8722.70653846154 243.206234190682 35.8654726408971 Trimmed Mean ( 24 / 24 ) 8719.44458333333 236.166583671586 36.9207380984035 Median 8641.33 Midrange 11756.04 Midmean - Weighted Average at Xnp 8765.48216216216 Midmean - Weighted Average at X(n+1)p 8825.5063888889 Midmean - Empirical Distribution Function 8765.48216216216 Midmean - Empirical Distribution Function - Averaging 8825.5063888889 Midmean - Empirical Distribution Function - Interpolation 8825.5063888889 Midmean - Closest Observation 8765.48216216216 Midmean - True Basic - Statistics Graphics Toolkit 8825.5063888889 Midmean - MS Excel (old versions) 8856.72552631579 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/17/t1268839640vgslvbx2vu05qpc/1y9pb1268839094.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/17/t1268839640vgslvbx2vu05qpc/1y9pb1268839094.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/17/t1268839640vgslvbx2vu05qpc/2m8941268839094.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/17/t1268839640vgslvbx2vu05qpc/2m8941268839094.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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