Central Tendency Investeringsgoederen

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Wed, 10 Dec 2008 05:16:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/10/t12289115162r867tl3rsbcijr.htm/, Retrieved Wed, 10 Dec 2008 12:18:38 +0000

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/2008/Dec/10/t12289115162r867tl3rsbcijr.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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97,7 101,5 119,6 108,1 117,8 125,5 89,2 92,3 104,6 122,8 96,0 94,6 93,3 101,1 114,2 104,7 113,3 118,2 83,6 73,9 99,5 97,7 103,0 106,3 92,2 101,8 122,8 111,8 106,3 121,5 81,9 85,4 110,9 117,3 106,3 105,5 101,3 105,9 126,3 111,9 108,9 127,2 94,2 85,7 116,2 107,2 110,6 112,0 104,5 112,0 132,8 110,8 128,7 136,8 94,9 88,8 123,2 125,3 122,7 125,7 116,3 118,7 142,0 127,9 131,9 152,3 110,8 99,1 135,0 133,2 131,0 133,9 119,9 136,9 148,9 145,1 142,4 159,6 120,7 109,0 142,0

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 113.733333333333 1.95455624719699 58.1888259784987 Geometric Mean 112.388228869872 Harmonic Mean 111.038385072555 Quadratic Mean 115.069084992398 Winsorized Mean ( 1 / 27 ) 113.741975308642 1.90701180523379 59.644085577487 Winsorized Mean ( 2 / 27 ) 113.7 1.87797582782009 60.543910265331 Winsorized Mean ( 3 / 27 ) 113.625925925926 1.83327338098757 61.9798045966918 Winsorized Mean ( 4 / 27 ) 113.507407407407 1.80274891072401 62.9635146260171 Winsorized Mean ( 5 / 27 ) 113.674074074074 1.76245022500223 64.4977500422345 Winsorized Mean ( 6 / 27 ) 113.703703703704 1.75725431562048 64.7053205065286 Winsorized Mean ( 7 / 27 ) 113.522222222222 1.62933941018446 69.6737717829891 Winsorized Mean ( 8 / 27 ) 113.522222222222 1.62595650861308 69.818732309793 Winsorized Mean ( 9 / 27 ) 113.433333333333 1.57295428579002 72.1148315358455 Winsorized Mean ( 10 / 27 ) 113.408641975309 1.53236704408941 74.008797313114 Winsorized Mean ( 11 / 27 ) 113.367901234568 1.50812698318442 75.1713234353722 Winsorized Mean ( 12 / 27 ) 113.353086419753 1.4915338099533 75.9976647282988 Winsorized Mean ( 13 / 27 ) 113.385185185185 1.44119518206663 78.6744131510308 Winsorized Mean ( 14 / 27 ) 113.523456790123 1.37298592289203 82.6836276303546 Winsorized Mean ( 15 / 27 ) 113.097530864198 1.30727779466878 86.5137703137169 Winsorized Mean ( 16 / 27 ) 113.216049382716 1.24383598318104 91.0216868731942 Winsorized Mean ( 17 / 27 ) 113.153086419753 1.21046502443053 93.4790218106354 Winsorized Mean ( 18 / 27 ) 113.308641975309 1.13255855533747 100.046608134575 Winsorized Mean ( 19 / 27 ) 113.214814814815 1.10621994429578 102.343856118855 Winsorized Mean ( 20 / 27 ) 113.214814814815 1.09263261069212 103.616543847341 Winsorized Mean ( 21 / 27 ) 113.240740740741 1.07496738075371 105.343420431364 Winsorized Mean ( 22 / 27 ) 112.996296296296 0.95367295887157 118.485373046541 Winsorized Mean ( 23 / 27 ) 113.308641975309 0.883974605681816 128.180879006035 Winsorized Mean ( 24 / 27 ) 113.338271604938 0.88029100109495 128.750914713387 Winsorized Mean ( 25 / 27 ) 113.338271604938 0.872322301231622 129.927059579833 Winsorized Mean ( 26 / 27 ) 113.209876543210 0.789607663434924 143.374845237353 Winsorized Mean ( 27 / 27 ) 113.076543209877 0.738663857973957 153.082544907542 Trimmed Mean ( 1 / 27 ) 113.656962025316 1.84890880171005 61.472454412135 Trimmed Mean ( 2 / 27 ) 113.567532467532 1.78099295071419 63.7664132370602 Trimmed Mean ( 3 / 27 ) 113.496 1.71980246089616 65.9936257684262 Trimmed Mean ( 4 / 27 ) 113.447945205479 1.66820603520956 68.0059553862172 Trimmed Mean ( 5 / 27 ) 113.430985915493 1.61847929165071 70.0849164401744 Trimmed Mean ( 6 / 27 ) 113.373913043478 1.57206085408917 72.1180180452784 Trimmed Mean ( 7 / 27 ) 113.307462686567 1.51813746225001 74.6358386536589 Trimmed Mean ( 8 / 27 ) 113.269230769231 1.48626228900419 76.2107950980322 Trimmed Mean ( 9 / 27 ) 113.228571428571 1.44853940344594 78.1674086042886 Trimmed Mean ( 10 / 27 ) 113.198360655738 1.41466073053986 80.018027087342 Trimmed Mean ( 11 / 27 ) 113.169491525424 1.38192864965487 81.8924273360187 Trimmed Mean ( 12 / 27 ) 113.143859649123 1.34669840764442 84.0157373075305 Trimmed Mean ( 13 / 27 ) 113.118181818182 1.30651846951060 86.5798566632998 Trimmed Mean ( 14 / 27 ) 113.086792452830 1.26696338146941 89.2581380857857 Trimmed Mean ( 15 / 27 ) 113.037254901961 1.23131672160195 91.8019327755888 Trimmed Mean ( 16 / 27 ) 113.030612244898 1.19977394441660 94.2099241035447 Trimmed Mean ( 17 / 27 ) 113.010638297872 1.17214523811175 96.4135114176847 Trimmed Mean ( 18 / 27 ) 112.995555555556 1.1429492046454 98.863147282746 Trimmed Mean ( 19 / 27 ) 112.962790697674 1.12062622530026 100.80327244475 Trimmed Mean ( 20 / 27 ) 112.936585365854 1.09591679015602 103.052153576163 Trimmed Mean ( 21 / 27 ) 112.907692307692 1.06503365602535 106.013262274788 Trimmed Mean ( 22 / 27 ) 112.872972972973 1.02668340229024 109.939415326268 Trimmed Mean ( 23 / 27 ) 112.86 1.00415272198786 112.393262029483 Trimmed Mean ( 24 / 27 ) 112.812121212121 0.988156739573791 114.164197534876 Trimmed Mean ( 25 / 27 ) 112.754838709677 0.963772144463968 116.993253392263 Trimmed Mean ( 26 / 27 ) 112.689655172414 0.928428207585301 121.376811100454 Trimmed Mean ( 27 / 27 ) 112.629629629630 0.901499460219112 124.935881383950 Median 111.9 Midrange 116.75 Midmean - Weighted Average at Xnp 112.6225 Midmean - Weighted Average at X(n+1)p 112.936585365854 Midmean - Empirical Distribution Function 112.936585365854 Midmean - Empirical Distribution Function - Averaging 112.936585365854 Midmean - Empirical Distribution Function - Interpolation 112.936585365854 Midmean - Closest Observation 112.659523809524 Midmean - True Basic - Statistics Graphics Toolkit 112.936585365854 Midmean - MS Excel (old versions) 112.936585365854 Number of observations 81

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289115162r867tl3rsbcijr/1hvbu1228911388.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289115162r867tl3rsbcijr/1hvbu1228911388.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289115162r867tl3rsbcijr/2bxta1228911388.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289115162r867tl3rsbcijr/2bxta1228911388.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')

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Software written by Ed van Stee & Patrick Wessa

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